
r NOSTRAND'S SCIENCE SERIES. 

78. SO Cts. 

THE 

HUH -ENGINE INDICATOR, 

AND ITS USE. 
& <£utue to practical OTorfcttifl lEitfltneers 

FOR 

GREATER ECONOMY AND THE BETTER WORKING 
OF STEAM-ENGINES. 



The Indicator, and what its Object is.; it-: C. struction 

and Action Thoroughly Explained : tcgethir with 

the Method of Calculating the Horse-Power 

of Engines as shown by the Diagrams. 



By William Barnet Le Van. 



ILLUSTRATED WITH TWENTY ENGRAVINGS. 



REPRINTED PROM " THE MECHANICAL ENGINEER, WITH 
MUCH ADDITIONAL MATTER. 



&m*. 



New York : 
D. VAN NOSTRAND, PUBLISHER, 

23 Murray and 27 Warren Street. 

1381. 



VAN ROSTRAND'S SCIENCE SERIES. 



No. 1, 

No. 2.- 

No. 3.- 

No. 4.- 

No. 5.- 

No. I 

No. \ 

No. ! 
No. \ 

No. 



2. 



No. 11, 
No. 12. 
No. 13 
No. 14, 
No. 15 
No. 16, 





-CHIMNEYS FOR FURNACES, EIRE- 
PLACES, AND STEAM BOILERS. By 
R. Armstrong, C. E. 

-STEAM BOILER EXPLOSIONS. By Ze- 

RAH COLBURN. 

-PRACTICAL DESIGNING OF RETAIN- 
ING WALLS. By Arthur Jacob, A. B, 

-PROPORTIONS OF PINS USED IN 
BRIDGES. By Charles Bender, C. E. 

-VENTILATION OF BUILDINGS. By W. 
F. Butler. 

™™^ T Q- 

IS. 

LIBRARY OF CONGRESS. , „, 

,S. 

w 

L. 

3F 
3D 
E. 

am 
the .French ot A. mallet, witn inustra- 
tions* 

THEORY OF ARCHES. By Prop. W. 
Allan. 
A THEORY OF VOUSSOIR ARCHES. 
By Prop. W. E. Cain. 
—GASES MET WITH ]N COAL MINES. 

By J. J. Atkinson. 
—FRICTION OF AIR IN MINES. By J. J. 

Atkinson. 
-SKEW ARCHES. By Prof. E. W. Hyde, 

C. E. Illustrated. 
—A GRAPHIC METHOD FOR SOLVING 
CERTAIN ALGEBRAICAL EQUA- 
TIONS. By Prof. George L. Vose. 
With Illustrations. 

— 



Shelf .x.Li.5 



UNITED STATES OF AMERICA. 



VAN NOSTRAND'S SCIENCE SERIES. 



No. 17.— WATER AND WATER SUPPLY, By 
Prof. W. H. Corfield, M. A., of the 
University College, London. 

No. 18.— SEWERAGE AND SEWAGE UTILI- 
ZATION. By Prof. W. H. Corfield, 
M. A., of the University College, Lon- 
don. 

No, 19. -STRENGTH OF BEAMS UNDER 
TRANSVERSE LOADS. By Prof. 
W. Allen, Author of " Theory of 
Arches.'' With Illustrations. 

No. 2a— BRIDGE AND TUNNEL CENTRES. 
By John B. McMasters, C. E. With 
illustrations. 

No. 2L— SAFETY VALVES. By Richard H. 
Buel, C. E. With Illustrations. 

No. 2% —HIGH MASONRY DAMS. By John B. 
McMasters, C. E. With Illustrations. 

No. 23.— THE FATIGUE OF METALS UNDER 
REPEATED STRAINS, with various 
Tables of Results of Experiments. From 
the German of Prof. Ludwig Spangen- 
berg. With a Preface by S. H. Shreve, 
A. M. With Illustrations. 

No. 24. -A PRACTICAL TREATISE ON THE 
TEETH OF WHEELS, with the Theo- 
ry of the Use of Robinson's Odonto- 
graph. By S. W. Robinson, Prof, of 
Mechanical Engineering. Illinois In- 
dustrial University. 

No. 25.— THEORY AND CALCULATIONS OF 
CONTINUOUS BRIDGES. By Mans- 
field Merriman, C. E. With Illustra- 
tions. 

No. 26.— PRACTICAL TREATISE ON THE 
PROPERTIES OF CONTINUOUS 
BRIDGES. By Charles Bender, C. E . 

No. 27.— ON BOILER INCRUSTATION AND 
CORROSION. By F. J. Rowan. 



THE 

Mechanical Engineer, 

EGBERT P. WATSON & SON, 
Editors and Proprietors, 

150 NASSAU STREET, NEW YORK. 



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The editors and proprietors are machinists and engineers 
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While not claiming to comprise in themselves all that is 
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" The Mechanical Engineer " circulates all over the United 
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Now in its Seventh Volume, and Rapidly Increasing 
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Published fortnightly at §2 per annum; §1 for six months. 



THE 

STEAM-ENGINE INDICATOR 

AND ITS USE. 
& @utti£ to Practical ratorfu'txg lEngmeers 

FOR 

GREATER ECONOMY AND THE BETTER 
WORKING OF STEAM-ENGINES. 



the indicator, and what its object is; its 

construction and action thoroughly 

explained; together with the 

method of calculating the 

horse-power of engines 

as shown by the 

diagrams. 



BV X 

William Barnet Le Van. 



ILLUSTRATED WITH TWENTY ENGRAVINGS: 



REPRINTED FROM "THE MECHANICAL ENGINEER," WITH 
MUCH ADDITIONAL MATTER. 



I 




NEW YORK : 

D, VAN NOSTRAND, PUBLISHER, 

23 Murray and 27 Warren Streets. 

18S4. 



r 



(i&> 



By D. VAN NOSTRAND. 



rq 



xt 



^J 




Lfc£ 



ELECTROTYPED AND PRINTED 

BY RAND, AVERY, & COMPANY, 

BOSTON, MASS. 



PEEFAOE. 



At the request of Egbert P. Watson, 
editor of 4 ' The Mechanical Engineer, ' ' the 
author prepared for publication in that 
journal a series of articles on "The Steam- 
Engine Indicator," which were published, 
and attracted the attention of readers inter- 
ested or engaged in the study and the use 
of marine, locomotive, and stationary en- 
gines. These articles, rewritten, revised, 
with much additional matter, make up this 
treatise, which is intended as elementary. 

As connected with the use and applica- 
tion of the indicator, an endeavor has been 
made to explain the most important parts 
of the theory and action of steam, and to 

show the modes of working engines that 

iii 



IV 

have been found to be the most advanta- 
geous, either for the development of power, 
or the saving of expense. The author 
has taken whatever he deemed valuable or 
necessary for the work from the best ac- 
credited writers on these topics, and offered 
suggestions of his own ; his purpose being 
to so treat the whole subject as to make 
it easily understood by even those least 
familiar with the operation of steam, and 
practically useful to those whose educa- 
tion has been, and must be, rather in the 
engine-room than in the class-room. 

W. Baknet Le Van. 
Philadelphia. 



THE 

STEAM-ENGINE INDICATOR, 

AND ITS USE. 



Before entering upon the subject of the 
action of steam in the cylinder of an engine, 
a few preliminary observations will be neces- 
sary to guard against mistakes which some- 
times arise with reference to the technical 
terms, and scales of measurement of press- 
ures, temperatures, etc. 

ELEMENT. 

The term " element," as used, means a 
body which cannot, as far as we know, be 
divided or decomposed. It is unalterable 
and indestructible, and therefore called a 
simple body, or element. 

A first or constituent principle of any 
thing ; that which admits not of division 
or decomposition into two or more ingredi- 
ents of unlike properties ; a simple or unde- 



compounded body, — as, " The elements of 
frater are oxygen and hydrogen." 

Formerly, and still in popular language, 
earth, air, loater, and fire are called the 
four elements, because they were formerly 
deemed first principles. 

"The elements be kind to thee!" 

Shakspeare. 

The proper habitation or sphere of any 
thing ; suitable state. . 

"A fish is out of his element when he is not in 
the water." — Milton. 

Elements, however, combine with one 
another, and lose their individuality, so to 
speak, in the compound. Thus two simple 
bodies, gases, hydrogen and oxygen, unite 
in certain definite proportions, and form 
water ; but the water can be again decom- 
posed into its constituents. 

Air is called a compound : it is a mix- 
ture of gases which preserve their individu- 
ality, as sand and sugar would do if they 
were mixed in a vessel. 

The principal material elements required 
for the support of life are oxygen, hydrogen, 



nitrogen, and carbon; and the simple physi- 
cal elements are force, velocity, and time, 
which constitute the functions light, heat, 
poiver, space, and work. 

THE PROOF OF ATMOSPHERIC PRESSURE. 

The real cause of atmospheric pressure is 
the weight of the atmosphere. When the air 
is removed from any surface of a body, the 
pressure of the air at once manifests itself. 

The removal of the air from any body 
produces in the space from which it is taken 
a condition which is called a "vacuum." 
The literal meaning of the term vacuum 
is a condition of space unoccupied by mat- 
ter, "empty." The utility of this natural 
phenomenon was experimented on as far 
back as 1634, by Torricelli, a pupil of 
the renowned astronomer and philosopher 
Galileo, in the following manner : — 

A glass tube about three feet long, and 
about one-quarter inch internal diameter, 
was sealed at one end, and filled with mer- 
cury. The open end being stopped by 
placing the thumb over it, the tube was 
then inverted ; and the lower end, covered 



by the thumb, was inserted in a vessel con- 
taining mercury. The tube still remaining 
vertical, the thumb being removed, the mer- 
cury sank about six inches from the sealed 
end, which showed about thirty inches 
(29.9218 exact) of mercury in the tube 
from the level of that in the vessel. The 
mass in the tube was, therefore, held by 
the atmosphere ; or, the pressure of the lat- 
ter on the mercury in the vessel prevented 
that in the tube descending below the six 
inches alluded to. Now, if the top end of 
the tube had been opened, the mercury in 
it would have sunk into the vessel, because 
the pressure of the atmosphere would have 
been in equilibrium on the inside and out- 
side of the tube ; and thus the mercury 
would fall, owing to gravity. 

The application of this experiment for 
practical purposes was thus carried out : A 
tube one square inch in area, filled as be- 
fore, and inverted likewise in a vessel of 
suitable dimensions, retained the mercury 
thirty inches high (29.9218) under the same 
circumstances. Then, as two cubic inches 
(2.036 exact) of mercury equals about one 



pound avoirdupois weight, and there are 
thirty cubic inches resisting the atmos- 
phere, the matter is resolved into a simple 
calculation. Thus : — 

W — weight of the mercury in the tube. 
C = cubic inches of mercury to equal one pound. 
x = pressure of the atmosphere in pounds per 
square inch. 

Then — 

w 30 • I , ■ _ 

x = -~- — -jr — lo pounds on the square inch. 

This is termed a perfect vacuum ; or, by 
using the above exact fractions, it will be 
14.7 pounds nearly. 

STEAM. 

Its density is equal to the pressure of the 
atmosphere, or 15 (14.72 exact) pounds per 
square inch ; and, unless confined, the tem- 
perature of water cannot be raised above 
the boiling point. The addition of 1° in the 
temperature of steam will increase its vol- 
ume 0.00202 of the volume occupied by the 
fluid at 32°. 

One cubic inch of water, evaporated un- 
der ordinary pressure of atmosphere, is con- 
verted into 1,700 cubic inches of steam, or 



6 



nearly one cubic foot. It exerts a mechani- 
cal force equal to raising 2,120.14 pounds 
one foot high. 

One cubic foot of steam, evaporated in 
one hour, is equal to one horse- power ; 
27,222 cubic inches of steam, at atmos- 
pheric pressure, equals one pound avoirdu- 
pois ; one pound of water, heated from 32° 
to 212°, requires as much heat as would 
raise 180 pounds 1°. 

One pound of water at 212°, converted 
into steam at 212° (pressure of 14.72 
pounds), absorbs as much heat for its 
conversion as will raise 966.6 pounds of 
water 1°. Steam at a pressure of one 
pound per square inch will support a col- 
umn of mercury (60° Fah.) 2.0376 inches. 

HEAT AND WORK. 

The earliest philosophers discredited the 
materiality of heat, and their theories ap- 
proached very closely to those now uni- 
versally accepted. These, however, were 
suppositions only, until Benjamin Thomp- 
son — Count Rumford — proved in 1798, 
experimentally, that heat could not be a ma- 



terial substance, but was probably a mani- 
festation of work. Sir Humphry Davy, a 
little later (1799), published the details of 
an experiment which conclusively confirmed 
these deductions from Rumford's work. 

Bacon and Newton, and Hook and Boyle, 
seem to have anticipated — long before 
Rumford's time — all later philosophers, in 
admitting the probable correctness of that 
modern dynamical, or vibratory, theory of 
heat which considers it a mode of motion ; 
but Davy, in 1812, for the first time stated 
plainly and precisely the real nature of heat, 
saying, " The immediate cause of the phe- 
nomenon of heat, then, is motion ; and the 
laws of its communication are precisely the 
same as the laws of the communication of 
motion." The basis of this opinion was 
the same that had been noted by Rumford. 

Dr. Mayer of Heilbronn, in 1842, sug- 
gested the identity of heat with ivork. 
James Prescott Joule of Manchester, in 
1843, proved, by a long series of experi- 
ments, that the production of heat was 
attended by the disappearance of a definite 
amount of mechanical zvork. 



8 



The labors of Mayer and Joule resulted 
in the important discovery of the dynamical 
value of heat, or, as it is usually termed, 
the mechanical equivalent of heat. This 
was found after making a very large num- 
ber of experiments, conducted in a great 
variety of ways : a weight of one pound 
falling through 772 feet would raise one 
pound of water through 1° Fah. ; or, what 
is just the same thing, a weight of 772 
pounds falling through one foot. 

The knowledge which this law gives us 
is exceedingly valuable. From it we learn 
that, in the very best engines that can be 
made, we are getting only about ten per 
cent of the whole power out of the coal which 
is in it. 

We will take a condensing engine aver- 
aging 85 horse-power, with a consumption 
per hour of 153 pounds of coal ; and the con- 
sumption per hour per horse-power would 

be — 

W = 1.8 pounds. 

The best anthracite coal contains ninety 
per cent of carbon. Throwing away the 
other constituents, we are burning ninety 



per cent of 1.8 pounds of pure carbon; 

or, 

1.8 X 0.90 = 1.62 pounds. 

Experiments show that a pound of car- 
bon generates, while burning to carbonic 
acid, 14,500 units of heat, — that is, it 
gives off as much heat as will raise 14,500 
pounds of water 1° Fah. ; and therefore 
1.62 pounds will generate — 

14,500 X 1.62 = 23,490 units of heat. 

We are therefore generating, in round 
numbers, 24,000 units of heat, and getting 
in exchange one indicated horse-power. 

Above we have seen that one unit of heat 
is equivalent to 772 pounds raised one foot 
high ; and, therefore, 24,000 units of heat 
are equivalent to — 

24,000 x 772 = 18,696,000 foot-pounds. 

But an indicated horse-power means 33,000 
pounds raised one foot high per minute, 
which is equivalent to 33,000 multiplied by 
60 minutes, — 

33,000 X 60 = 1,980,000 foot-pounds per hour. 
From this we see that we are burning coal 



10 



sufficient to raise 18,696,000 foot-pounds. 
Therefore we are, in fact, out of one of the 
very best engines, getting but one-ninth, or 
about ten per cent, of the power we should 
do. 

VAPORS. 

A vapor is a gas at a temperature near 
to that at which condensation occurs. All 
bodies assume the gaseous condition at suit- 
able temperatures. In an intensely heated 
furnace (that of the electric light) even 
carbon has been made to appear as a gas, 
although only in a small quantity. Most 
solids liquefy before becoming gaseous ; but 
some appear to become gases at once, and 
are said to sublime. 

According to Professor James Thomson, 
this always occurs when the boiling point 
of the substance at the given pressure is 
lower than the freezing point for the same 
pressure. 

Vapors are formed more readily in vacuo 
than in air ; but, for any given temperature, 
the quantity of vapor which will form in a 
space from an exposed liquid is the same, 



11 



whether air or other gases be present or not, 
— the vapor being formed almost instan- 
taneously in the second case, and requiring 
more or less time for formation in the first. 

The pressure which this vapor eventually 
adds to the pressure of gases already exist- 
ing in the space depends on the temperature 
only, and is the same, no matter what may 
have been the previously existing pressure. 
When no more liquid will change into vapor, 
we may say that the space is saturated. 

A space unsaturated with vapor may be 
contracted, the pressure becoming greater 
until the maximum pressure for that tem- 
perature is reached. After this, contraction 
at constant temperature causes some of the 
vapor to be condensed to the liquid state, 
as the pressure has reached its maximum, 
and the space has become saturated. 

Unsaturated vapors follow approximately 
the laws of gases in expanding with heat. 
Steam, when passing along hot pipes to the 
engine, may be superheated; and its co- 
efficient of expansion will be found to differ 
very little from that of common air. By 
superheating steam we increase its volume, 



12 



whilst its pressure is unchanged. We also 
render it less liable to condense in the cylin- 
der ; and we convert into steam many par- 
ticles of water which are often carried over 
from the foam in the boiler. 

LOW PRESSURE AND HIGH PRESSURE. 

Steam, or the vapor of water, when 
produced at the usual pressure of the at- 
mosphere, is commonly denominated loiv- 
pressure; in opposition to that which is 
formed at a higher pressure than that of 
the air, and accordingly named high-press- 
ure steam. In common language, however, 
the term ' c low-pressure steam ' ' is applied 
to the steam which has even a pressure 
of several pounds on the square inch, 
and is therefore formed at a temperature 
higher than 212°. The steam-engines sup- 
plied with a condenser, when first made, 
used low-pressure steam, and by condens- 
ing the exhaust gained the additional 
pressure nearly due to the atmosphere ; and 
were usually called low-pressure engines, 
instead of condensing engines, their proper 
name. In the present advanced state of 



13 



engineering, high- pressure steam is now 
most generally used for supplying con- 
densing engines. They are called condens- 
ing and non-condensing engines, 

ABSOLUTE PRESSURE. 

It is customary to express the elastic 
force of steam in three ways ; namely, in 
pounds of pressure that it exerts on the 
square inch, in the height of the column 
of mercury which it sustains, and in at- 
mospheres. (The actual pressure of the 
atmosphere is continually varying, the bar- 
ometric column fluctuating generally be- 
tween 28.5 and 30.5 inches in height ; these 
points in either direction being, however, 
but rarely reached, and still more rarely 
passed.) This is simple and convenient 
for most purposes relating to the boiler, but 
leads to misconception when applied to 
steam in the cylinder of an engine. Water 
evaporated in the open air is said, accord- 
ing to this notation, to be transformed into 
steam of zero pressure, instead of steam 
of 14.7 pounds pressure, per square inch; 
which pressure counterbalances that of the 



14 



atmosphere. If such steam is used in a 
condensing engine, the effect is said to be 
due to vacuum, which is still regarded by 
some people as a separate force uncon- 
nected with steam, and in fact operating 
on the other side of the piston. When 
steam of higher pressure is used, it is 
customary, in finding the horse-power, to 
add the vacuum to the steam pressure., — so 
carrying out the same idea. 

The absolute pressure of steam is meas- 
ured from zero, or perfect vacuum, and 
consists of the pressure as shown by the 
steam-gage (which only shows the press- 
ure above atmosphere) ; and, as before 
stated, the pressure of the atmosphere is 
indicated by the barometer. The latter 
may, for all practical purposes, be taken at 
15 pounds, corresponding to 30.6 inches of 
mercury. The vacuum gages in general 
use are usually graduated to agree with the 
scale of barometer, and the vacuum is usu- 
ally stated in inches of mercury. To the 
steam pressure shown by gage, add 15 
pounds for total pressure. Thus, if the 
pressure gage indicates 75 pounds, the 
total, or absolute, pressure is 90 pounds. 



15 



When the piston moves forward in an en- 
gine, the total pressure on steam side at any 
point in the stroke of piston is the press- 
ure above the atmosphere, plus 15 pounds ; 
and the total pressure for whole stroke is 
the mean pressure above the atmosphere, 
plus 15 pounds. Thus, if the mean pressure 
for whole stroke is 25 pounds, the total 
mean pressure is 40 pounds ; and this 40 
pounds, whether the engine is operated 
condensing or " low-pressure," or non-con- 
densing or " high-pressure," is the variable 
factor in estimating the load on the engine. 

Now, if the engine be operated non- 
condensing, the 15 pounds (pressure of 
atmosphere) on steam side is balanced by 
a like pressure of atmosphere on exhaust 
side of piston ; and its effect is annihilated, 
or reduced to nothing. But, if the engine 
be operated condensing, a large proportion 
of the pressure of atmosphere on exhaust 
side of piston is removed, and an equivalent 
portion of the pressure of atmosphere on 
steam side of piston made to do useful 
work. With well-proportioned condensing 
apparatus, the pressure of atmosphere on 



16 



exhaust side of piston can be reduced 
nearly ninety per cent : in other words, a 
vacuum in the exhaust end of cylinder of 
(13 pounds) 26.5 inches may be main- 
tained ; and this 26.5 inches, or 13 pounds 
per square inch of piston, is an absolute 
gain, and should in all cases be utilized. 

PROPERTIES OF STEAM. 

Total pressure, or absolute pressure, 
means the steam pressure in pounds per 
square inch, including the pressure of the 
atmosphere, and is generally denoted by P; 
and p is used to denote the steam pressure 
above atmosphere, as is shown on the ordi- 
nary spring-gage. If a mercury column 
is used, it is shown in inches and fractions 
of inch. The specific gravity of mercury 
at 32° Fah. is 13.5959, compared with water 
of maximum density at 39°. One cubic 
inch of mercury weighs 0.49086 pounds ; 
of which a column of 29.9218 inches is 
a mean balance of the atmosphere, or 
14.68757 pounds per square inch, very 
nearly. 

It is common to say that an atmosphere 



17 



is 15 pounds on the square inch, or 30 
inches of mercury. This is not correct ; the 
pressure of 15 pounds on the square inch 
being equal to that of a column of mercury 
30.55 inches in height. One pound press- 
ure on the square inch is equal to 2.037 
inches of mercury. 

The French use a column of mercury 
760 millimetres in height, at the tempera- 
ture of 0° C, or 32°Fah., which is as nearly 
as possible the mean atmospheric pressure. 

EXPANSIVE POWER OF STEAM. 

When a volume of air is compressed into 
a smaller volume, a certain amount of power 
is expended in compressing it, which pow- 
er, as in the case of a bent spring, is given 
back when the pressure is withdrawn. If, 
however, compressed air is suddenly re- 
leased into the atmosphere, the power ex- 
pended in compressing it is lost. If this 
power can be utilized, it will be clear gain. 
This gain can be effected if, instead of re- 
leasing the compressed air, it is permitted 
to expand to its original volume. Now, the 
steam used to propel engines is in the con- 



18 



dition of air already compressed ; and, to 
save the power which would be lost if the 
steam were suddenly released into the 
atmosphere, it must be used expansively ; 
and, to use it expansively, it must be cut 
off, — that is, the steam port must be closed 
before the piston has completed its stroke. 
If the flow of steam to an engine be cut off 
when the piston has performed half-stroke, 
leaving the stroke to be completed by the 
expanding steam, it has been found by 
experiment that the efficacy of a given 
quantity of steam will be increased 1.7 
times beyond what it would have been if 
the steam at half- stroke had been released 
into the atmosphere, instead of allowed to 
expand in the cylinder. If cut off at one- 
third of the stroke, the efficacy will be 
increased 2.1 times; at one-fourth stroke, 
2.4 times ; at one-fifth, 2.6 times ; at one- 
sixth, 2.8 times ; at one-seventh, 3 times ; 
and at one-eighth, 3.2 times. 

LATENT HEAT OF STEAM. 

In generating steam from water, there is 
absorbed about five and a half times as 



19 



much heat as is required, under atmospheric 
pressure, to raise the temperature of the 
water from freezing point, 32° Fah., to boil- 
ing point, 212° Fah., — an amount of heat 
which, if the water were a fixed solid, would 
render it red-hot by daylight. Tested by 
a thermometer, the steam will show only 
212° of sensible heat. It has been found, 
however, by experiment, that, when the 
steam from a pound of water at 212° is 
returned by condensation to water, sufficient 
heat is set free to raise the temperature of 
5J pounds of water from 32° to 212° : thus 
proving that the steam has absorbed five 
and a half times as much heat, in becoming 
steam, as the water from which it is pro- 
duced exhibited in passing from 32° to 
212°; and that, in the process of wholly 
evaporating into steam any given quantity 
of water, 1,000° of heat are absorbed. But, 
as the thermometer indicates only 212° of 
heat in steam, it follows that this prodi- 
gious excess of heat — the difference be- 
tween 212° and 1,000° — must be stored up 
in the steam in some hidden, unaccount- 
able way and condition, and is called the 
latent heat of steam. 



20 



TO WORK STEAM EXPANSIVELY. 

If we take an upright cylinder one inch 
in diameter and at least 1,700 inches in 
height, pour into it one cubic inch of water ; 
fit into it a steam-tight piston, resting on 
the water, so counterbalanced as to be 
weightless, and so arranged as to work with- 
out friction ; and then place a lamp under 
the cylinder, — we then notice, that, so 
soon as the water reaches the temperature 
of 212°, it will begin to boil, and produce 
steam, and the steam will begin to push up 
the piston. So long as the lamp continues 
to burn, and the water continues to boil, 
so long will the steam continue to push up 
the piston, until all of the water has been 
evaporated into steam. When all of the 
water has so evaporated, it will be found 
that from one cubic inch of water there has 
been produced 1,700 cubic inches of steam ; 
and as this would fill 1,700 cubic inches of 
the cylinder, and as the pressure of the at- 
mosphere — the only resistance in this case 
to be overcome — is 15 pounds (14.7 ex- 
act) to the square inch, this experiment 
would show that one cubic inch of water, 



21 



wholly evaporated into steam, will push or 
lift, say, 15 pounds 1,700 inches, or 142 
feet. If, now, the experiment be carried 
a little farther with a similar cylinder and 
piston, and 15 pounds be loaded on the 
piston, making, with atmospheric pressure, 
30 pounds, we shall find that under this 
additional pressure the temperature of tlte 
water must be raised to 252°, instead of 
212°, before it begins to boil, and before 
the steam begins to push up the piston ; 
and that, when the whole of the water is 
evaporated, there will be only 850 instead 
of 1,700 cubic inches of steam, and the 
piston will be pushed or lifted up only 
850 instead of 1,700 inches, or, in round 
numbers, 71 feet. If, then, one cubic inch 
of water, wholly evaporated, will produce 
steam enough to push or lift 15 pounds 
142 feet, and 30 pounds 71 feet, it would 
produce steam enough to push or lift 142 
times 15 pounds, or 2,130 pounds (say one 
ton) one foot. When, then, the steam 
from one cubic inch of water has pushed 
or lifted one ton one foot, it has done all it 
can do ; and, if the experiment is to be re- 



22 



peated, this spent steam must be released 
by means of a valve, called the exhaust 
valve, and new steam admitted, or gener- 
ated, to push or lift up the piston. The 
machinery used in this experiment repre- 
sents simply a full-stroke, or non-expan- 
sion, engine, making one stroke ; and, for 
ejich stroke made by such an engine, the 
utmost possible power to be got is equiva- 
lent to one ton lifted one foot for every 
cubic inch of water evaporated, — no more, 
no less. This is all the power we can get 
out of a steam-engine without a cut-off. 

But let us experiment a little farther. 
Suppose we load the piston with one ton of 
bricks, and suppose, instead of opening the 
exhaust valve, we remove one of the bricks : 
the load being thus, to this extent, dimin- 
ished, the steam, no longer compressed by 
the whole ton, will expand a little, and 
push or lift up the rest of the bricks a 
little farther ; and, as brick after brick is 
removed, the steam will push or lift up 
the rest of the bricks farther and farther, 
until, the last brick having been removed, 
it will be found that the steam has pushed 



23 



or lifted up the piston to the full height of 
1,700 inches, or 142 feet. Now, it will be 
seen from this experiment, that all the 
power which was produced by the steam as 
the bricks were successively removed was a 
clear gain, as it cost no fuel or steam other 
than that which had already pushed or 
lifted the one ton one foot, and can do no 
more unless and until the steam was re- 
lieved of a part or the whole of the resist- 
ing weight or pressure. This principle, the 
law of expanding steam, was discovered by 
James Watt. 

RATE OF EXPANSION. 

The higher the grade, or ratio, of expan- 
sion, the greater is the economy ; but the 
result is somewhat modified by other con- 
siderations. 

First, The higher the rate of expansion, 
the lower is the mean or average pressure 
throughout the stroke ; and a low mean 
pressure involves the use of a large engine 
for a given power. 

Second, With a high rate of expansion, 
the mean pressure is much lower than the 



24 



initial pressure ; and, although the power 
of the engine is only due to the mean 
pressure, the strength of the engine must 
be sufficient to withstand the initial press- 
ure. 

Third, A very high rate of expansion 
also leads to a very low final pressure ; and 
as to drive the engine itself against its own 
friction only, and to expel the steam from 
the cylinder, seldom require less than 
three pounds above the external pressure, 
it follows, that, if the steam is so far 
expanded that the terminal pressure falls 
below this, the expansion is excessive, and 
the reverse of advantageous. 

In non-condensing engines, the lowest 
final pressure is determined by the pressure 
of the atmosphere, say 15 pounds per square 
inch ; and 18 pounds may be taken as the 
lowest pressure to which steam can be ex- 
panded with advantage. If the exhaust 
passages are small, or the exhaust steam 
damp, a higher final pressure will be more 
economical. In condensing engines, the 
temperature of the condenser is generally 
about 100° Fah., and the pressure corre- 



25 



sponding to this is about one pound per 
square inch ; but the presence of air in the 
condenser generally prevents the pressure 
there falling below two pounds per square 
inch. From four to five pounds may be 
taken as the lowest advantageous final 
pressure. 

Fourth, The highest advantageous rates 
of expansion, even with jacketed cylinders, 
appear, in practice, to be between 12 and 
16 times. Higher rates are, and should be, 
aimed at ; but, with our present arrange- 
ment of engine, it is doubtful- whether the 
•increased economy of very high ratios, or 
grades, pays for the increased complication 
and the extra cost of the apparatus re- 
quired to attain it. In un jacketed cylin- 
ders the limit of advantageous expansion is 
much under the lowest of the grades named. 

In practice, the best result of steam- 
engines does not convert more than ten per 
cent of the heat used by it into work ; and 
this in engines of considerable size, and with 
boilers and furnaces fairly efficient. In 
small engines it is much less ; indeed, it is 
certain that few among the thousands of 



26 



steam-engines in daily use below five horse- 
power give an efficiency greater than Jive 
per cent. The great cause of loss is the 
amount of heat necessary to change the 
water from the liquid to the gaseous state, 
most of this being rejected with the exhaust 
either into the condenser or the atmosphere. 
Many attempts have been made to use 
liquids of lower specific heat than water, 
and requiring less heat for evaporation, — 
the principal being alcohol, ether, and car- 
bon bi-sulphide ; but, for obvious reasons, 
no success has been attained. 

TEMPERATURE OF STEAM. 

When steam is generated in a boiler, the 
water is heated until it arrives at the tem- 
perature of ebullition, and the elevation of 
temperature is sensible to the thermometer. 
Next, the water is converted into steam by 
an additional absorption of heat, which is 
not measured by the thermometer, and is 
therefore called latent. The heat is not, in 
fact, latent, but is appropriated in convert- 
ing water into steam of the same tempera- 
ture. 



27 



The pressure, as well as the density, of 
steam which is generated over water in a 
boiler, rises with the temperature ; and, re- 
ciprocally, the temperature rises with the 
pressure and density. There is only one 
pressure and one density for each tempera- 
ture ; and thus it is that steam, produced 
in a boiler over water, is always generated 
at the maximum density and maximum 
pressure corresponding to its temperature. 
In such condition, steam is said to be satu- 
rated, being incapable of vaporizing more 
water into the same space, unless the tem- 
perature be raised. Saturation is therefore 
the normal condition of steam generated in 
contact with a store of water, and the same 
density and the same pressure are always 
to be found in conjunction with the same 
temperature. 

In consequence, saturated steam over 
water stands both at the condensing point 
and at the generating point ; that is, it is 
condensed if the temperature falls, and more 
water is evaporated if the temperature rises. 

If saturated steam is separated from 
water in a space of fixed dimensions, if an 



28 



additional quantity of heat be supplied to 
the steam, the state of saturation ceases : 
the steam becomes superheated, and the 
temperature and the pressure are increased, 
whilst the density is not increased. Steam, 
thus surcharged with heat, approaches to 
the condition of a perfect gas. 

TOTAL UNITS OF HEAT IN STEAM. 

The total heat of steam consists of its 
latent heat, in addition to its sensible heat. 
The latent heat of saturated steam at 32° 
Fan., the freezing-point, was experiment- 
ally determined by Regnault to be equal to 
606.5° C. (centigrade) ; or such that the 
total heat of one pound of saturated steam 
at 0° (zero) C. would be capable of raising 
the temperature of 606.5 centigrade pounds 
of water 1°. 

At higher temperatures, the total heat of 
saturated steam was found to increase uni- 
formly between the temperature 0° C. and 
204.44° C. at the rate of 0.305° for each 
addition of temperature of one degree ; 
and, therefore, if the temperature in de- 
grees be multiplied by 0.305 (its specific 



29 



heat), and 606.5 be added to the product, 
the sum will express the total heat of satu- 
rated steam at the given temperature ; or, 

H=z 606.5 + 0.305 T°, 

where H equals the total heat of steam, and 
T° degrees centigrade, which, for Fahren- 
heit scale, will be as follows : — 

# = g ( 606.5 + 0.305 r o ); 
or 

H = 1091.7 + 0.305(r°- 32°); 
or 

U= 1082 + 0.3057°. 

In which T° being the temperature as read 
on Fahrenheit scale, and H being the total 
heat, or the heat necessary to convert one 
pound of water at the freezing-point into 
saturated steam at the temperature T°. 

That is to say, that steam at 32° Fah., 
the freezing-point, will be equal to 1,082° ; 
or that the total heat of one pound of satu- 
rated steam at 32° Fah. would be capable of 
raising the temperature of 1,082 pounds of 
water 1°. The water from which the steam 
is generated is supposed to be supplied at 
the temperature of 32° Fah. 

The expression of the total heat repre- 



30 



sents units of heat when the weight of the 
steam is one pound. 

If the water to be evaporated is supplied 
at any higher temperature than 32°Fah., 
the total heat to be expended in evaporat- 
ing it is found by deducting the difference 
of temperature from the total heat. 

Examjrte. — Water is to be supplied at 
60°, which is (60-32) 28° above 32° 
Fah. Then, 1,082 - 28 = 1,054. 

Before Regnault made his experiments, it 
was supposed that the total heat of steam, 
or the sum of its sensible and latent heat, 
was the same for all temperatures ; but 
these experiments prove that it increases 
with the increase of temperature in the uni- 
form ratio of 0.305 of a degree for each 
degree of sensible heat : so that, as steam 
expands in volume, of each one degree of 
temperature that it loses, 0.6065 parts only 
become latent, or are converted into in- 
ternal work ; and the remaining 0.305 parts 
are set free, and are capable of being con- 
verted into mechanical work. 



31 



Table No. 1. 

PROPERTIES OF STEAM, 



Total 
pressure 

in 
pounds 

per 
square 
inch. 


Tem- 
pera- 
ture. 
Fah- 
ren- 
heit. 


Volume 
water 
equal 
1 at 40. 


Units of heat from 32° to J°. 


Press- 
ure 
above 

atmos 
phere- 


Total 


Latent 


per 
pound. 


per 

cubic 
foot. 


per 
pound. 


per 

cubic 
foot 


P 


rpO 


V 


H 


w 


L 


U 


P 


14.7 
15.0 
20.0 
25.0 
30.0 
35.0 
40.0 
45.0 
50.0 
55.0 
60.0 
65.0 
70.0 
75.0 
80.0 
85.0 
90.0 
95.0 
100.0 
105.0 
110.0 
115.0 


212.0 
213.0 
228.5 
241.0 
251.4 
260.7 
268.9 
276.2 
282.8. 
289.0 
294.7 
300.0 
305.0 
309.8 
314.3 
318.4 
322.4 
326.2 
329.9 
333.3 
336.8 
340.0 


1740.0 
1706.0 
1288.0 
1035.0 
866.7 
745.8 
654.9 
584.1 
527.2 
480.6 
441.6 
408.7 
380.4 
355.8 
334.3 
315.2 
298.2 
283.0 
269.4 
257.0 
245.7 
235.3 


1146.6 
1147.0 
1151.7 
1155.7 
1158.7 
1161.5 
1164.0 
1166.2 
1168.4 
1170.1 
1171.9 
1173.5 
1175.0 
1176.5 
1177.8 
1179.1 
1180.3 
1181.5 
1182.7 
1183.7 
1184.7 
1185.7 


41.100 
41.920 
55.802 
69.632 
83.410 
97.156 
110.87 
124.57 
138.27 
151.91 
165.56 
179.13 
192.71 
206.29 
219.84 
233.38 
246.94 
260.46 
273.93 
287.40 
300.87 
314.33 


965.7 
965.1 
954.1 
945.4 
937.8 
931.2 
925.3 
920.1 
915.4 
910.9 
906.9 
903.0 
899.4 
896.0 
892.7 
889.8 
886.9 
884.2 
881.6 
879,1 
876.5 
874.2 


34.61 
35.29 
46.23 
56.96 
67.51 
77.89 
8S.14 
98.28 
108.3 
118.3 
128.1 
137.8 
147.5 
157.1 
166.6 
176.1 
185.4 
194.9 
204.2 
213.4 
222.6 
231.8 


0.0 
0.3 
5.0 
10.0 
15.0 
20.0 
25.0 
30.0 
35.0 
40.0 
45.0 
50.0 
55.0 
60.0 
65.0 
70.0 
75.0 
80.0 
85.0 
90.0 
95.0 
100.0 



HEAT : ITS MECHANICAL EQUIVALENT. 

Heat is dynamic work, or the product of 
the three simple elements, — force, velocity, 



32 



and time; in which the temperature of the 
heat represents force, and the cubic con- 
tents of the units of heat represent the 
product of time and velocity, which is sjxice, 

It has been shown that the change of heat 
equal to one pound of loater raised in tem- 
perature one degree is one unit of heat. 

For water, the quantity of heat, measured 
by heat units, corresponding to any change 
of heat, may then be represented by the 
number of pounds of water multiplied by 
the number of degrees of the thermometer, 
which indicates the change of temperature. 

Joule, in his experiments, found that 
one unit of heat developed 772 foot-pounds 
of work ; water being taken at a tempera- 
ture of 39.1° Fah., its point of maximum 
density. 

The English unit of dynamic ivorli is one 
pound lifted twelve inches, or one pound of 
force acting through one foot of space, and 
is called the foot-pound ; 550 per second, 
or 33,000 foot-pounds or units of work, 
performed in one minute, make a horse- 
power. 

The French unit of work is one kilo- 



33 



gram lifted one metre, called the kilo- 
gram-metre, or, for brevity, kilo-metre. 
It is equal to 7.233136 foot-pounds. Sev- 
enty-five kilogram-metres, exerted in one 
second, constitute the French horse-power, 
equal to 32,549,112 foot-pounds per minute. 

The English horse-power is therefore 
1.01416 French horse-powers, and the 
French horse-power is 0.986 of an English 
horse-power. 

One horse- power will consume, or gener- 
ate, 2,564 calorics (or heat) per hour. 

Table No. 2. 

COMPARISON OF DIFFERENT UNITS OF HEAT 

AND WORK. 



English Calorics. 


French Caloric. 


Prussian 


Dynamic Work. 


Fah. 
pounds. 


Cent, 
pounds. 


Fah. 
kilo. 


Cent. 
kilo. 


Cent, 
p. ft. 


Foot 
pounds. 


Kilo- 
metres. 


1 
1.8 

2.2047 
3.968 
17.33 
O00L2953 
0.0093896 


0.5555 

1 
1.2248 
2.2047 

0.9630 

0.0007196 

0.0005205 


4536 
0.8165 

1 
1.8 

0.7862 
00005876 
0.0004250 


252* 
0.4536 
0.555 
1 
0.4368 
0.000326 
0.0002361 


0.5769 
1.0385 
12719 

2.2894 

1 
0.0007473 
0.0005405 


772.0 
13896 
1702.0 
3063.6 
1368.2 
1 
7.233 


106.51 
191.71 

384 066 
626.52 
273.66 
0.13823 

1 



MECHANICAL POWER. 

Mechanical power, or work, is pressure 
acting through space ; and the law of the 



34 



conservation of force teaches that power, 
once produced, cannot be annihilated, 
though it may be transformed into other 
forces of equivalent value. In all machines 
a certain proportion of the power resident 
in the prime mover is lost ; while the rest 
is utilized, and is rendered available for the 
performance of those labors for which pow- 
er is required. Thus, in a water-wheel, the 
theoretical value of the fall is that due to 
a certain weight of water falling through a 
certain number of feet in the minute ; and 
if we know the height of the fall, and the 
discharge of water in a given time, the theo- 
retical value of such a fall can be easily 
computed. But by no machine, whether a 
water-wheel or a turbine, can the whole of 
the power be extracted from the fall, 
and be made available for useful purposes. 
About eighty per cent of the theoretical 
power of a water- fall is considered to be a 
very satisfactory result to obtain in prac- 
tice ; and the rest is lost by impact and 
eddies, and by the friction of the water 
and of the machine. 
In the steam-engine, the motive force is 



35 



not gravity, but heat ; and just in the same 
way as power is imparted by water in de- 
scending from a higher to a lower level, so 
is power imparted by heat in descending 
from a higher to a lower temperature. 
These two temperatures are the tempera- 
ture of the boiler, and the temperature of 
the atmosphere or condenser ; and it is 
clear, that, if the atmosphere or condenser 
were as hot as the boiler, there would be 
no motion to the engine. And just as in 
a water-fall there is a certain theoretical 
power due to the quantity of gravitating 
matter and the difference of level, so in a 
steam-engine there is also a certain theo- 
retical power clue to the quantity of heated 
matter and the difference of temperature. 
But, in utilizing the power of steam-boilers, 
this theoretical limit is not approached so 
nearly as in hydraulic machines. In the 
steam-boiler, the larger part of the attain- 
able fall of temperature is lost. Thus, if 
we suppose the temperature of the furnace 
to be 2,000° Fah., and the temperature of 
the boiler to be 300° (corresponding to 50 
pounds per square inch above the atmos- 



36 



phere), while that of the condenser is 100°, 
we utilize pretty effectually the power rep- 
resented by the difference in temperature 
between 100° and 300° ; but the difference 
between 300° and 2,000° is not utilized 
at all. The consequence of this state of 
things is ' that not above one-tenth of the 
power, theoretically due to the fuel con- 
sumed, is utilized in the best modern steam- 
engines, — the rest being thrown away. 

THE WORK OF EXPANSION. 

When the valve for admission of steam 
to an engine-cylinder is open during the 
full stroke of the piston, the cylinder is 
filled with steam at every stroke, of a 
pressure nearly equal to that of the boiler. 
See Fig. 1. 

In order to save steam, — or, more 
correctly, to employ its effect to a higher 
degree, — the admittance of steam to the 
cylinder is cut off when the piston has 
moved a portion of its stroke. From the 
cut-off point the steam acts expansively, 
with a decreased pressure on the piston, as 
shown in diagram (Fig. 2). 



37 



If we admit steam of 85 + 15 = 100 
pounds total pressure per square inch into 
a cylinder, and the valve closes the steam- 
port when the piston has travelled half the 
length of the stroke, from B to e, the steam 
remaining in the cylinder will expand to 
double its volume in forcing the piston to 

Fig. I 




the end of the cylinder ; and a certain 
amount of work has been done with half 
the quantity of steam, as in case of Dia- 
gram 2 ; and the steam, in expanding after 
the port was closed during the rest of the 
stroke, continues to do work, as the press- 
ure of the expanding steam is greater than 



38 



that of the condenser. Now, this work 
performed after the steam was cut off is 
greatly in excess of that performed in Fig. 
2, as compared to their respective volumes 
(as 5 is to 10), and has been obtained by 
the use of expansion. In this latter case 

Fig.2 




the steam expanded twice its volume, and 
its pressure was exactly half what it was 
before ; namely, 50 pounds per square inch. 
In making this calculation for pressure 
of steam after it has expanded, the total 
pressure, P, must be used, which is reck- 
oned from perfect vacuum. 



39 



In Fig. 1, VB is the diameter, and VV 
the length, of the cylinder ; the pressure 
during the stroke, when there is no expan- 
sion, is assumed at 85 pounds, as per steam- 
gage, plus 15 pounds fo'r perfect vacuum, 
equals 100 pounds total pressure per square 
inch. 

Now, if the steam is cut off when the 
piston has moved one-half the length of 
the cylinder (see Fig. 2), from B to e, the 
steam, whose volume is F, 22, e, and m, 
must expand and fill the whole cylinder, its 
pressure getting less and less : so that such 
lines as em, 12,3 4, and gV, in Figs. 2 and 
3, represent pressures at different parts of 
the stroke, and the curve e, 1, 3, /*, and g 
is the expansion curve. 

Diagram Fig. 3 represents the same en- 
gine cutting off at one-quarter the stroke, 
the average pressure being 59.65 pounds 
mean pressure. 

In fact, Figs, 1, 2, and 3 are imaginary 
indicator diagrams, supposed to be taken 
from a condensing engine (the average 
pressure from a non-condensing engine 
would be arrived at in the same way, but 



40 



15 pounds would be deducted after the cal- 
culations were made, to allow for pressure 
of the atmosphere) ; and hence their areas 
indicate the relative amounts of work per- 




formed in a single stroke of the engine, 
when there is : — 

First, No cut off. 

Second, Cut off at half stroke. 

Third, Cut off at one-fourth of the 
stroke. 

Now, the area of Fig. 2 is nearly equal 
to that of Fig. 1 ; so that, when expansion 
is allowed, a cylinder half full of steam will 



41 



perform more than three-fourths as much 
work as the cylinder full of steam, at the 
same initial pressure, can perform without 
expansion. 

As a further illustration, Fig. 3 is the 
diagram that would be made if the steam 
were cut off after the piston had travelled 
one-fourth of the stroke. In this case, only 
one-fourth the steam would be required, as 
was for Fig. 1, performing more than one- 
half as much as the latter with one-fourth 
of the steam. 

Assuming that, in the cylinder, the vol- 
ume of steam varies inversely as the press- 
ure, the work done in one stroke of the 
piston is : — 

AlPil + x) (1). 

Or, in words, the work done is the value of. 
the hyperbolic logarithm x, from Table 4, 
p. 47, plus one, multiplied by the product 
of the initial pressure P, multiplied by I 
(the distance the piston moves before steam 
is cut off) , and this product by the area, A, 
of the cylinder in square inches. 



42 



Where A = area of cylinder, or piston, in square 
inches. 
L == length of stroke of piston in inches. 
I — distance travelled by the piston be- 
fore the steam is cut off. 

g = grade, or ratio, of expansion, y, 

x — hyperbolic logarithm of g (see Table 
No. 4). 

P = initial pressure of steam in pounds 
per square inch, measuring from 
perfect vacuum in cylinder before 
cut-off takes place. 

p = Mean average pressure after cut off 
takes place and during full stroke, 
in pounds per square inch; and is 
found by the following formula : — 

p=z-(l + x) (2). 

y 



HYPERBOLIC LOGARITHMS. 

In estimating the power which an engine 
will exert with a given pressure of steam, 
to be cut off at any given point of the 
stroke, we ascertain the mean pressure on 
the square inch which will be exerted dur- 
ing the stroke, by means of the table of 
hyperbolic logarithms, which latter are cal- 
culated for expansion according to the law 
of Boyle and Mariotte. 



43 



Table No. S. 
HYPERBOLIC LOGARITHMS 



No. 


Loga- 


No. 


Loga- 


No. 


Loga- 


No. 


Loga- 


rithms. 


rithms. 


rithms. 


rithms. 


0.0 


0.00000 


4.0 


1.38629 


70 


1.94591 


10 


2.30258 


1.1 


0.09530 


4.1 


1.41096 


7.1 


1.96006 


11 


2.39589 


1.2 


0.18213 


4.2 


1.43505 


7.2 


1.97406 ! 


12 


2.48491 


1.3 


0.26234 


4.3 


1.45859 


7.3 


1.98787 


13 


2.56494 


1.4 


0.33646 


4.4 


1.48161 


74 


2.00149 ! 


14 


2.63906 


1.6 


0.40505 


4.5 


1.50408 


i 7.5 


2.01490 i 


15 


2.70S05 


1.6 


0.46998 


4.6 


1.52603 


7.6 


2.02816 


16 


2.77259 


1.7 


0.53063 


4.7 


1.54753 


7.7 


2.04115 


17 


2.83321 


1.8 


0.5S776 


4.8 


1.56859 


7.8 


2.05415 


18 


2.S9037 


1.9 


0.64181 


4.9 


1.5S922 


7.9 


2.06690 


19 


2.94444 


2.0 


0.69315 


5.0 


1.60944 


8.0 


2.07944 


20 


2.99573 


2.1 


0.74190 


5.1 


1.62922 


8.1 


2.09190 


21 


3.04452 


2.2 


0.78843 


5.2 


1.64865 


8.2 


2.10418 ! 


22 


3.09104 


2.3 


0.83287 


5.3 


1.66770 


8.3 


2.11632 J 


23 


3.13549 


2.4 


0.S7544 


5.4 


1.68633 


| 8.4 


2.12S30 ! 


24 


3.17805 


2.5 


0.91629 


5.5 


1.70475 


8.5 


2.14007 


25 


3.21888 


2.6 


0.95 548 


5.6 


1.72276 


8.6 


2.15082 j 


26 


3.25810 


2.7 


0.99323 


5.7 


1.74046 


8.7 


2.16338 1 


27 


3.29584 


2.S 


1.02962 


5.S 


1.75785 


8.8 


2.17482 ! 


28 


3.33220 


2.9 


1.06473 


5.9 


1.77495 


8.9 


2.18615 


29 


3.36730 


3.0 


1.09861 


6.0 


1.79175 


1 9.0 


2.19722 


30 


3.40120 


3.1 


1.13140 


6.1 


1.80S27 


| 9.1 


2.20837 


31 


3.43399 


3.2 


1.16314 


6.2 


1.82545 


9.2 


2.21932 


32 


3.46574 


3.3 


1.19594 


6.3 


1.84055 


1 9-3 


2.23014 


33 


3.49651 


3.4 


1.22373 


6.4 


1.S5629 


1 9.4 


2.24085 


34 


3.52636 


3.5 


1.25276 


6.5 


1.87180 


; 9.5 


2.25129 


35 


3.55535 


3.6 


1.28090 


o.d 


1.88658 


9.6 


2.26191 


36 


3.58352 


3.7 


1.30834 


6.7 


1.90218 


9.7 


2.27228 


37 


3.61092 


3.8 


1.33046 


6.8 


1.91689 


9.8 


2.28255 


38 


3.63759 


3.9 


1.36099 


6.9 


1.93149 


9.9 


2.29171 


39 


3.66356 



MEAN PRESSURE. 



When the steam is expanded in the 
cylinder, the mean pressure p, throughout 
the stroke of piston, will be less than the 
initial pressure P. The mean pressure p, 



44 



during expansion, will be according to 
formula (2) ; or, in words : — 

Rule, — Divide the initial pressure P, by 
the proportion, or grade, #, of the stroke 
during which the steam is admitted, and 
multiply the quotient by hyperbolic loga- 
rithm a?, plus one (take the value of x from 
Table No. 4). 

RATIO, OR GRADE, OF EXPANSION. 

The proportion, or grade, g, of the stroke 
during which the steam is admitted, is found 
by dividing the length L in inches of the 
cylinder swept through by the piston, by the 
length I in inches of the space into which 
the steam is admitted. 

Example. — Suppose the length of the 

stroke of a given engine be L = 80 inches, 

the initial pressure P, 90 pounds per square 

inch, and the steam to be cut off at I = 20 

inches of the stroke : what will be the mean 

pressure ? 

p 

Formula (2) '== p = — (1 + «)". 

y 
Grade, or ratio, g, = f § = 4 grade, or ratio, 
of expansion. 
Hyperbolic logarithm of 4 = 1.386 (see x in Table 

No. 4). 



45 

Then we have 

p = \*x (1+1.386) = 53.68 pounds, 

the mean pressure required. 

The initial pressure P, given above, is 
the total pressure, measured from perfect 
vacuum. To find the initial P, add the 
atmospheric pressure — in common practice 
an atmosphere is generally taken as 15 
pounds (14.7 exact) per square inch — to 
the pressure p, shown by the steam-gage ; 
and from the mean pressure found as above 
subtract the counter or back pressure, to 
effective mean pressure exerted. Thus, in 
the above case, the steam -gage is sup- 
posed to show a pressure p of 90 — 15 = 75 
pounds only ; and, if the calculation is being 
made for a condensing, or " low-pressure," 
engine, the estimated loss from imperfect 
vacuum must be subtracted (not less than 
four pounds) , and if for a non-condensing, 
or "high-pressure," engine, the pressure of 
the atmosphere, and also any estimated 
counter or back pressure above that, must 
be subtracted from 53.68 pounds, the" mean 
pressure obtained by the calculation. 



46 



HYPERBOLIC LOGARITHMS, 

The hyperbolic logarithm of a number is 
found by multiplying the common logarithm 
of the number by 2.30258509. 

Example. — The common logarithm of 
3 is 0.4771213, which, multiplied by 
2.30258509, gives 1.09861, the hyperbolic 
logarithm. 

And, also, the hyperbolic logarithm, mul- 
tiplied by 0.43329448, gives the common 
logarithm. 

The following, Table No. 3, contains the 
hyperbolic logarithms for numbers running 
from 1.11, the grade, or ratio, of -^, or 0.9 
cut off, up to y 1 ^, or 0.1, representing T ^ 
cut off, which is considered sufficient for 
application to expansion of steam for all 
practical purposes. 

EXPANSION OF STEAM, AND ITS EFFECT WITH 
EQUAL VOLUMES OF STEAM. 

The theoretical economy of using steam 
expansively is as follows, the same volume 
of steam being expended in each case, and 
expanded to fill the increased spaces : — 



47 



Table No. 4. 



Portion of 
stroke at 

which 
steam is 
cut off. 


Grade, 
or ratio, 

of ex- 
pansion. 


Hyper- 
bolic 
loga- 
rithm. 


Mean 
pressure 
of steam 

during 
the 

whole 

stroke. 


Percent- 
age of 
gain in 
fuel, or 
power. 


1 


9 


X 


P 


% 


ITT, or 0.1 


10.0 


2.302 


3.302 


230.0 


i , or 0.125 


8.0 


2.079 


3.079 


208.0 


i , or 0.166 


6.0 


1.791 


2.791 


179.0 


-To, or 0.2 


5.0 


1.609 


2.609 


161.0 


i , or 0.25 


4.0 


1.386 


2.386 


139.0 


to, or 0.3 


3.33 


1.203 


2.203 


120.0 


^ , or 0.333 


3.0 


1.099 


2.099 


110.0 


| , or 0.375 


2.66 


0.978 


1.978 


97.8 


A, or 0.4 


2.5 


0.916 


1.916 


91.6 


i , or 0.5 


2.0 


0.693 


1.693 


69.3 


A, or °- 6 


1.666 


0.507 


1.507 


50.7 


f , or 0.625 


1.6 


0.47 


1.47 


47.0 


| , or 0.666 


1.5 


0.405 


1.405 


40.5 


•f -, or 0.7 


1.42 


0.351 


1.351 


35.1 


| , or 0.75 


1.33 


0.285 


1.285 


22.3 


ft, or 0.8 


1.25 


0.223 


1.223 


20.5 


I , or 0.875 


1.143 


0.131 


1.131 


13.1 


ft, or 0.9 


1.11 


0.104 


1.104 


10,4 



48 



In Table No. 4 no deductions are made 
for a reduction of the temperature of the 
steam while expanding, or for loss by back 
pressure. 

The same relative advantages follow in 
expansion, as above given, whatever may 
be the initial pressure of the steam. 

The pressure of the atmosphere is to be 
included in calculating the expansion. It 
must, therefore, be deducted from the re r 
suits in non-conclensing engines. In con- 
densing engines a deduction must be made 
for imperfect vacuum. This will amount 
to about (2^ pounds per square inch) 5 
inches in well-proportioned engines. 

Where there is no cut-off, as in diagram 
Fig. 1, the work done equals APL, or the 
area, A, of the cylinder, multiplied by the ab- 
solute pressure P, and 'this product by the 
length of stroke, X, of the piston in feet. 

When the cut-off takes place at one- 
fourth of the stroke L, at point e, diagram 
Fig. 3, there is only one-fourth as much 
steam admitted as in case of diagram Fig. 

APL 

1 ; but the work, instead of being — - — , or 



49 

= 25, will be, as before stated, 

AIP{1 +x), or 1 x 0.25 X 1(1 + 1.386) 
= 59.65. 

To make this more clear to the student 
and general reader, we will assume an en- 
gine doing actual work. It is well known 
that the most convenient way of calcu- 
lating the horse-power of an engine is to 
multiply the area of the cylinder in square 
inches by the speed of the piston in feet 
per minute, and divide the product by 
33,000. The result so obtained will be the 
horse-power of one pound mean effective 
pressure, and is called the horse-power 
constant, which, if multiplied by the whole 
mean effective pressure on the piston dur- 
ing the stroke, will give the indicated horse- 
power of the engine. 

For example, suppose that the engine 
that would produce indicator diagrams as 
represented by Figs. 1, 2, and 3, had a 
stroke L = 3 feet, making 100 revolutions 
per minute, and a diameter of cylinder 
A = 110 square iuches, and a piston speed 
of 100 x 3 x 2 = 600 feet per minute : then 



50 

the horse-power value of one pound mean 
effective pressure will be as follows : — 

110 x 600 
Horse-power constant = — 

oouuu 

= 2 horse-power. 

Now, diagram Fig. 1 averaged initial 
pressure P = 100 pounds, or a mean effec- 
tive pressure throughout the stroke. The 
horse-power, therefore, will be as fol- 
lows : — 

Horse-power = 100 X2 = 200 horse-power. 

In diagram Fig. 3, the steam was cut 
off after the piston had moved from B to e, 
or one-fourth of its stroke ; the grade, or 
ratio, of expansion being - 3 g 6 = 4. There- 
fore, the mean effective pressure p will be, 
according to formula (2) , — 

or, substituting values, 

p = -4 Q (l + 1.386) = 59.65 pounds; 

or, to simplify it still further, it will be as 
follows : — 

2f = 4 hyper, logarithm of 4 = 1.386 + 1 = 2.386. 



51 
Then 



-MP = 25 X 2.386 = 59.65 pounds. 

Now, diagram Fig. 3 shows a mean 
effective pressure of 59.65 pounds, which, 
multiplied by the horse-power constant, 
will be, — 

P = 59.65 X2 = 119.30 horse-power. 

Therefore, we see that one- fourth of the 
steam expanded performs three-fifths, or 
nearly sixty per cent, of the whole work ; 
so that, by using expansion, the work ob- 
tained from one pound of steam is 2.386 
times what was obtained when following 
full stroke, as shown by diagram Fig. 1, 
or a gain of forty per cent by using steam 
expanding three-fourths of the stroke. 

„ 200-119.30 fAR 

% — — — 40. o per cent gain. 

The number 2.386 has lately been called 
the u indicator co-efficient" of the engine. 
By cutting off at one-tenth of the stroke, 
the efficiency of the steam is increased 3.3 
times ; that is, the " indicator co-efficient " 
is 3.3. 

Expansion is valuable in another way. 



52 



At the end of every stroke the piston stops 
momentarily, returning on its old path ; 
and it is advisable to prepare for the 
sudden reversal of motion of the piston, 
by diminishing the steam pressure. Now, 
when expansion is used, the greatest press- 
ure is exerted at the beginning of the 
stroke, when the piston moves slowly, and 
when it is most advisable to get up a great 
velocity. The pressure after cut off di- 
minishes gradually until it is very little 
greater than that of the atmosphere ; so 
that the steam experiences little difficulty 
in escaping by the exhaust-passages on the 
return stroke. In fast-running engines, 
the exhaust-port is opened before the end 
of the stroke, and the exhaust-port on the 
other side of the piston is closed, that there 
may be a cushion of the steam to prevent 
" shocks " or tfc jars." 

THE PERFORMANCE OF STEAM WHEN 
EXPANDED. 

Steam, in its ordinary condition as satu- 
rated steam, though it does not rank as a 
perfect gas, nevertheless acts in the cylin- 



53 



der of a steam-engine so much to the same 
effect as a perfect gas could do, that its 
performance may be treated in the same 
way as if it were perfect as a gas. The 
quality in consideration of which a gas is 
said to be perfect is, as has already been 
stated, its • property of expanding into a 
larger volume in the same proportion in- 
versely as the pressure falls, the tempera- 
ture being supposed to remain the same. 
Now, though saturated steam does not and 
can not exactly follow this ratio, seeing that 
the pressure falls more rapidly than the vol- 
ume increases, yet it is found that the work 
performed by steam by expansion in the cyl- 
inder of an engine is practically the same as 
if it acted on the principle of a perfect gas. 
Therefore it will be seen that the curve 
described by the pencil of an indicator, in- 
dicating the falling pressure of dry satu- 
rated steam expanding behind an advancing 
piston, is, if not exactly, nearly hyperbolic 
in its nature, or such that the products of 
the pressures at all points of the stroke, 
multiplied by the respective volumes of 
steam, are equal to each other. 



54 



Table No. 5. 

MEAN AND INITIAL PRESSURE IN THE 
CYLINDER. 

[Assuming that the pressures are inversely as the 
volume.! 



Portion of 

stroke at 

which 

steam is 

cut off. 


Grade, 
or ratio, 
of ex- 
pansion. 


Hyper- 
bolic 
loga- 
rithm. 


Mean 
pressure 

during 

stroke, 

the 

initial 
pressure 

being 

taken 

atl. 


Initial 
pressure 
in cylin- 
der, the 
mean 
pressure 
being 
taken 
as 1. 


1 


9 


X 


P 


P 


f , or 0.75 
■ftj or 0.7 

f , or 0.666 
A, or 0.6 

i , or 0.5 
A* or 0.4 

■J- , or 0.333 
A. or 0.3 

£ , or 0.25 
A, or 0.2 

-g- p or 0.166 

| , or 0.142 

| , or 0.125 


1.333 

1.428 

1.5 

1.666 

2.0 

2.5 

3.0 

3.333 

4.0 

5.0 

6.0 

7.0 

8.0 


0.2876 
0.3506 
0.4055 
0.5108 
0.6931 
0.9163 
1.0986 
1.2040 
1.3863 
1.6094 
1.7918 
1.9459 
2.0795 


0.965 
0.949 
0.937 
0.904 
0.846 
0.766 
0.669 
0.661 
0.596 
0.522 
0.465 
0.421 
0.385 


1.036 
1.054 
1.067 
1.106 
1.182 
1.305 
1.495 
1.513 
1.678 
1.916 
2.150 
2.375 
2.598 



55 



Table No. 5 — (continued). 



Portion of 

stroke at 

which 

steam is 

cut off. 


Grade, 
or ratio, 

of ex- 
pansion. 


Hyper- 
bolic 
loga- 
rithm. 


Mean 

pressure 
during 
stroke, 

the 

initial 

pressure 

being 

taken 

atl. 


Initial 
pressure 
in cylin- 
der, the 
mean 
pressure 
being 
taken 
as 1. 


1 


9 


X 


P 


P 


■g- , or 0.111 
Til, or 0.1 
-fi, or 0.09 
iV, or 0.083 
T3> or 0.076 
T4, or 0.071 
lV». or 0.066 
-^q, or 0.062 
-■rr, or 0.058 
TFs or 6.055 
-fV, or 0.052 
2V, or 0.05 
2^, or 0.047 
Y2> °r 0.045 
2^3, or 0.043 
^L, or 0.041 
2V, or 0.04 


9.0 
10.0 
11.0 

12.0 
13.0 
14.0 
15.0 
16.0 
17.0 
18.0 
19.0 
20.0 
21.0 
22.0 
23.0 
24.0 
25.0 


2.1972 
2.3025 
2.3979 
2.4849 
2.5649 
2.6391 
2.7081 
2.7726 
2.8332 
2.8904 
2.9444 
2.9967 
3.0445 
3.0910 
3.1355 
3.1781 
3.2189 


0.355 
0.330 
0.309 
0.293 
0.274 
0.260 
0.247 
0.236 
0.226 
0.216 
0.208 
0.200 
0.192 
0.186 
0.180 
0.174 
0.169 


2.817 

3.030 

3.236 

3.448 

3.649 

3.846 

4.048 

4.237 

4.425 

4.629 

4.807 

5.0 

5.208 

5.376 

5.555 

5.747 

5.917 



56 



DIAGRAM OF WORK DONE DURING EXPANSION. 

The hyperbolic curve of expansion, ex- 
pressive of the falling pressure, relative to 
the increasing volume, is represented by 
Dg on diagram Fig. 4. 

The rectangle ABCD is supposed to be 
the section of a cylinder, having a stroke 
of 24 inches. The diagram is divided into 
24 parts, or inches of stroke. During six 
of these, that is, six inches of the stroke, 
or one-fourth, AE, the steam is admitted ; 
and it is expanded during the remaining 
three- fourths, FC. Assuming that there 
is no clearance, the terminal pressure gC 
would be one-fourth of the initial pressure 
P, during admission ; that is, it would be 
equal to the initial pressure P, taken in 
this case at 100 pounds total pressure per 
square inch, multiplied by the period of ad- 
mission, and divided by the length, I = 6 
inches of the stroke, or 

100 X / 4 - = 25 pounds per square inch, 

the terminal pressure. 

The pressure for any intermediate point 
of the stroke may be found, similarly, by 



57 



Fig. 4. 



100 pounds absolute 


1 


100 


2 


100- 


3 


100 


& 


100 


5 


100 


ft 

F 
7 


^^\^ 85.71 


>v 75 


8 


>v 65.66 


9 


N. 60 


10 


\ 54.54 


11 


\ 50 


12 


\ 46.15 


13 


\ 42.85 


14 


\ 40 


15 


\ 37.5 


16 


\ 35.29 


17 


\ 33.33 


18 


\ 31.57 


19 


\ 30 


20 


\ 28.57 


21 


\ 27.27 


22 




26.08 


23 


25. 


24 



58 



taking the portion of the stroke described, 
from the commencement to the given point, 
as the divisor. Thus, at the end of 12 
inches of the stroke, the total pressure is — 

100 X ^ = 50 pounds per square inch. 

Finding the pressure similarly for each 
intermediate inch of the stroke, and draw- 
ing ordinates for each inch of stroke, the 
curve may be formed by tracing it through 
the extremities of the ordinates, as shown 
in the figure. 

The process of finding the intermediate 
pressures is, in fact, a case of proportion ; 
and the following statements, showing the 
proportional process for each of the ordi- 
nates, make it quite clear : — 

As 7 spaces : 6 spaces : : 100 lbs. pr. : 85.71 lbs. pr. at 7 inch. 

8 spaces : 6 spaces : : 100 lbs. pr. : 75.00 lbs. pr. at 8 inch. 

9 spaces : 6 spaces : : 100 lbs. pr. : 66.66 lbs. pr. at 9 inch. 

10 spaces : 6 spaces : : 100 lbs. pr. : 60.00 lbs. pr. at 10 inch. 

11 spaces : 6 spaces : : 100 lbs. pr. : 54.54 lbs. pr. at 11 inch. 

12 spaces : 6 spaces : : 100 lbs. pr. : 50.00 lbs. pr. at 12 inch. 

13 spaces : 6 spaces : : 100 lbs. pr. : 46.15 lbs. pr. at 13 inch. 

14 spaces : 6 spaces : : 100 lbs. pr. : 42.85 lbs. pr. at 14 inch. 

15 spaces : 6 spaces : : 100 lbs. pr. : 40.00 lbs. pr. at 15 inch. 

16 spaces : 6 spaces : : 100 lbs. pr. : 37.50 lbs. pr. at 16 inch. 

17 spaces : 6 spaces : : 100 lbs. pr. : 35.29 lbs. pr. at. 17 inch. 

18 spaces : 6 spaces : : 100 lbs. pr. : 33.33 lbs. pr. at 18 inch. 

19 spaces : 6 spaces : : 100 lbs. pr. : 31.57 lbs. pr. at 19 inch. 



59 



20 spaces : 6 spaces : : 100 lbs. pr. : 30.00 rbs. pr. at 20 inch. 

21 spaces : 6 spaces : : 100 lbs. pr. : 28.57 lbs. pr. at 21 inch. 

22 spaces : 6 spaces : : 100 lbs. pr. : 27.27 lbs. pr. at 22 inch. 

23 spaces : 6 spaces : : 100 lbs. pr. ; 26.08 lbs. pr. at 23 inch. 

24 spaces : 6 spaces : : 100 lbs. pr. : 25.00 lbs. pr. at 24 inch. 

Having got so far, the work done by 
expansion may be calculated from these 
particulars without the aid of hyperbolic 
logarithms. 



THE THEORETICAL POSSIBILITY OF GAIN BY 
EXPANSION. 

To find the increase of efficiency arising 
from using steam expansively : — 

Rule. — Divide the total length of the 
stroke by the distance (which call 1) 
through which the piston moves before the 
steam is cut off. The Napierian logarithm 
of the part of the stroke performed with 
the full pressure of steam before cut off 
represents the increase of efficiency due to 
expansion. 

Example. — Suppose that the steam be 
cutoff at T 2 n (two-tenths), or 0.2, of the 
stroke : what is the increase of efficiency 
due to expansion ? 

Now, 0.2 of the whole stroke is the same 



60 



as ^ of the whole stroke ; and the ratio, or 
grade, of expansion equals 5. The hyper- 
bolic logarithm of 5 is 1.609, which, in- 
creased by 1, the value of the portion 
performed with full initial pressure, gives 
1.609 + 1 = 2.609 as the relative efficacy 
of the steam when expanded to this extent 
(eight-tenths), instead of 1, which would 
have been the efficacy if there had been no 
expansion. 

If the steam be cut off at t x q, t %, t 3 q, t %, 
to> xo> to' to' or to of the stroke, the re- 
spective ratios, or grades, of expansion will 
be 10, 5, 3.33, 2.5, 1.66, 1.42, 1.25, and 
1.11 ; of which numbers the respective hy- 
perbolic logarithms are 2.303, 1.609, 1.203, 
0.916, 0.693, 0.507, 0.351, 0.223, 0.104: 
and, if the steam be cut off at ^, f, f, 
lb f ' f -> or i °f tne stroke, the respective 
ratios, or grades, of expansion will be 8, 4, 
2.66, 2, 1.6, 1.33, and 1.14 ; of which the 
respective hyperbolic logarithms are 2.079, 
1.386, 0.978, 0.693, 0.470, 0.285, 0.131. 
With these data, it will be easy to compute 
the mean pressure of steam of any given 
initial pressure when cut off at any eighth 



61 



part or any tenth part of the stroke ; as we 
have only to divide the initial pressure of 
the steam in pounds per square inch by the 
ratio of expansion, and to multiply the quo- 
tient by the hyperbolic logarithm, increased 
by 1, of the number representing the ratio, 
or grade, which gives the mean pressure 
throughout the stroke in pounds per square 
inch. Thus, if steam of 65 + 15 = 80 
pounds absolute be cut off at half-stroke, 
the ratio, or grade, of expansion is 2 ; and 
80 divided by 2 = 40, which, multiplied by 
1 + 0.693 = 67.72, which is the mean 
pressure throughout the stroke in pounds 
per square inch. The terminal pressure is 
found by dividing the initial pressure by 
the ratio, or grade, of expansion ; thus, the 
terminal pressure of steam of 80 pounds 
cut off at half-stroke will be 80 divided 
by 2 = 40 pounds per square inch. 

Example. — What will be the mean 
pressure, throughout the stroke, of steam 
of 160 pounds per square inch cut off at 
| the stroke? 

Divide 160 by 8 = 20, which, multiplied 
by 3.079 (the hyperbolic logarithm of 8 



62 



increased by 1, 2.079 + 1 = 3.079), gives 
61.58, which is the mean pressure exerted 
on the piston throughout the stroke, in 
pounds per square inch. If the steam 
were cut off at -^ of the stroke, instead 
of -|, then we should have 160 divided 
by 10 = 16, which, multiplied by 3.303 (the 
hyperbolic logarithm of 10 increased by 
1 = 2.303 + 1 = 3.303), gives 52.85 pounds, 
which would be the mean pressure on the 
piston throughout the stroke in such a case. 
If the initial pressure of the steam were 10 
pounds per square inch, and the expansion 
took place throughout T ^ of the stroke, or 
the steam were cutoff at T %, then 10 divided 
by 5 = 2, which, multiplied by 2.600 = 5.218 
pounds per square inch of mean pressure. 

GAIN IN FUEL BY EXPANSION. 

When steam is cut off before the end 
of the stroke in a cylinder, the pressure 
effected by it for the portion at which it 
flowed for full stroke is represented by 1 ; 
and the pressure exerted afterward, by the 
result due to the relative expansion. The 
total pressure, or work, is represented by 



63 



the sum of these units. If the steam had 
flowed for the full stroke of the piston, the 
pressure would have been 1 added to the 
proportionate distance for which the steam 
was expended in case of expansion. 

The gain of working steam expansively 
is as follows : — 

Cutting off at to the stroke, efficacy is increased 3.300 times. 
Cutting off at % the stroke, efficacy is increased 3.000 times. 
Cutting off at yg the stroke, efficacy is increased 2*600 times. 
Cutting off at 4 the stroke, efficacy is increased 2.386 times. 
Cutting off at -fu the stroke, efficacy is increased 2.200 times. 
Cutting off at f the stroke, efficacy is increased 1.980 times. 
Cutting off at -3% the stroke, efficacy is increased 1.920 times. 
Cutting off at -g the stroke, efficacy is increased 1.690 times. 
Cutting off at -fy the stroke, efficacy is increased 1.500 times. 
Cutting off at -§ the stroke, efficacy is increased 1.470 times. 
Cutting off at -/q the stroke, efficacy is increased 1.350 times. 
Cutting off at f the stroke, efficacy is increased 1.280 times. 
Cutting off at -fa the stroke, efficacy is increased 1.220 times. 
Cutting off at I the stroke, efficacy is increased 1.130 times. 
Cutting off at -^ the stroke, efficacy is increased 1.100 times. 

Table No. 6 shows the value of the 
portion of steam after cut off ; its relative 
efficacy by expansion being as # this indi- 
cates, instead of being one, which would 
have been the efficacy had there been no 
expansion. From the above we can com- 
pute the gain in fuel as follows : — 



64 



Rule. — Divide the relative effect, or, in 
other words, the number of times the effi- 
cacy is increased, by the grade of expan- 
sion g (see table of hyperbolic logarithms) , 
and divide 1 by the quotient. The result 
is the initial pressure of steam required to 
be expanded to produce a like effect of 
steam at full stroke. Divide this pressure 
by the number of times the steam is ex- 
panded, and subtract the quotient from 1. 
The remainder will give the percentage of 
gain of fuel. 

Example. — Suppose the steam in an 
engine to be cut off after the piston has 
moved one-fourth the length of the stroke, 
what is the gain in fuel ? 

The relative effect (see efficacy due to 

expansion, on p. 63) equals 2.386, and the 

number of times of expansion equals 4, 

Then 

2.386 -f- 4 = 0.5965, 
and 

1.00 -r 0.5965 == initial pressure = 1.64, 
and 

1.64 -f- 4 - 0.41, 
and 

1.00 — 0.41 = per cent = 59. 



65 

Table No. 6. 
MEAN PRESSURE OF EXPANDING STEAM. 



Abso- 
lute 


GRADE OF EXPANSION OF STEAM, DENOTED BY X. 


steam 
















press- 
ure 


4 


3 


2.666 


2 


1.6 


1.5 


1.333 


per 




















square 
inch. 


Steam cut off at I, from beginning of stroke. 


P 


1 

4 


J, 
3 


3 

8 


i 

2 


5 

8 


2 
3 


3 


or 


or 


or 


or 


or 


or 


or 




0.25 


0.333 


0.375 


0.50 


0.625 


0.666 


0.75 


20 


11.931 


13.991 


14.853 


16.931 


18.350 


18.734 


19.304 


25 


14.913 


17.488 


18.567 


21.164 


22.938 


23.481 


24.130 


30 


17.897 


20.986 


22.280 


25.396 


27.524 


28.100 


28.956 


35 


20.880 


24.484 


25.992 


29.630 


32.110 


32.784 


33.782 


40 


23.860 


27.964 


29.670 


33.860 


36.750 


37.333 


38.550 


45 


26.842 


31.459 


33.378 


38.092 


41.341 


42.000 


43.368 


50 


29.828 


34.977 


37.133 


42.328 


45.875 


46.835 


48.262 


55 


32.811 


38.474 


40.846 


46.561 


50.462 


51.518 


53.088 


60 


35.794 


41.972 


44.559 


50.794 


55.050 


56.202 


57.914 


65 


38.777 


45.470 


48.273 


55.027 


59.637 


60.885 


62.740 


70 


41.760 


48.967 


51.986 


59.260 


64.225 


65.569 


67.566 


75 


44.743 


52.465 


55.700 


63.493 


68.812 


70.252 


72.393 


80 


47.726 


55.963 


59.413 


67.726 


73.400 


74.936 


77.216 


85 


50.709 


59.461 


63.126 


71.959 


77.987 


79.619 


82.042 


90 


53.692 


62.958 


66.840 


76.192 


82.574 


85.303 


86.866 


95 


56.675 


66.456 


70.553 


80.425 


87.163 


89.986 


91.699 


100 


59.657 


69.954 


74.267 


84.657 


91.750 


93.670 


96.524 


105 


62.640 


73.451 


77.981 


88.890 


96.337 


98.353 


101.35 


110 


65.622 


76.949 


81.694 


93.123 


100.92 


103.04 


106.17 


115 


68.606 


80.447 


85.407 


97.356 


105.51 


107.72 


111.00 



TERMINAL PRESSURE. 

Rule for finding the pressure at the end 



68 



of the stroke, or at any point during ex- 
pansion : — 

P = initial pressure of steam in pounds per square 
inch, including the pressure of the atmos- 
phere. 

L — distance travelled by the piston when the 
pressure of steam = x> 
I — distance travelled by the piston before the 
steam is cut off. 

x = pressure of steam in the cylinder, including 
the pressure of the atmosphere when the 
piston has travelled a distance X. 

PI 

Or, in words, the terminal pressure for 
any cut off is the absolute pressure P, mul- 
tiplied by the distance Z, the piston has 
moved when steam is cut off, and this prod- 
uct divided by stroke L. 

The steam pressure on the boiler is read- 
ily known ; but the steam in its passage to 
the cylinder is subject to various losses, as 
"wire-drawing," condensation, friction, 
etc., so that frequently the pressure on the 
piston does not exceed two-thirds of that 
on the boiler* 



67 



Therefore, recourse must be had to the 
indicator for furnishing the exact data for 
ascertaining the exact pressure in the cylin- 
der, so as to ascertain the power exerted 
by the engine, namely, the mean or aver- 
age pressure of steam ; or, more accurately, 
the excess of pressure on the acting side of 
the piston to produce motive force. And 
from no other source can it be accurately 
ascertained. 

In every branch of science our knowledge 
increases as the power of measurement 
becomes improved ; and we have now to 
discuss the measuring instrument peculiarly 
appropriated to the steam-engine, namely, 
the indicator invented by Watt. The 
student must thoroughly understand the 
reading of an indicator diagram before he 
can appreciate the reason for the various 
methods of construction adopted with ref- 
erence to some of the working parts of an 
engine. 



68 



THE STEAM-ENGINE INDICATOR, AND ITS USE. 



The indicator is an instrument for show- 
ing the pressure of steam in the cylinder at 
all points in the stroke, and registering the 
varying pressures, as the piston moves to 
and fro, on a piece of paper secured to a 
revolving drum, by a pencil attached to the 
indicator piston. 

The indicator was invented and first used 
by James Watt. For some time it was 
kept by him a secret, but became known 
before his death ; and to its use, now quite 
general, we are more indebted than to any 
thing else for the degree of excellence 
which the steam-engine has attained. 

The improved forms of instruments, 
known as the "Thompson," "Crosby," 
and "Tabor" indicators, are now largely 
employed. Each consists of a small cylin- 
der accurately bored out, and fitted with a 
piston capable of working in the cylinder 



69 



with little or no friction, and yet practically 
steam-tight. The piston-rod is attached to 
a pair of light levers, so linked together 
that a pencil, carried at the end of one of 
the levers, moves in nearly a straight line 
vertically. A spiral spring placed in the 
cylinder above the piston, and of a strength 
proportioned to the steam pressure, resists 
the motion of the piston ; and the elasticity 
of this spring is such that each pound press- 
ure on the piston causes the pencil to move 
a certain fractional part of an inch. 

The paper is wound round the drum, 
parallel to, and connected by a bracket with, 
the cylinder of the instrument, which has a 
diameter of two inches, and is capable of 
a semi-rotatory motion upon its axis of such 
an extent that the extreme length of dia- 
gram may be five inches. Motion is given 
to the drum in one direction by means of a 
cord connected with a suitable part of the 
engine, revolving the same way with that 
of the piston of the engine ; and the drum 
makes its return movement by the action of 
a coiled spring at the base of the drum. 

The indicator may be fixed in any de- 



70 



sired position ; and the guide-pulleys, at- 
tached to the instrument at the base of the 
paper-drum, may also be placed so as to 
bring the cord upon the drum- pulley from 
any convenient direction. The upper end 
of the piston is open to the atmosphere ; the 
lower end may, by means of a three-way 
cock on it, be put into communication either 
with the atmosphere or the cylinder of the 
engine. When the key of the cock is so 
turned that both sides of the indicator 
piston are acted on by the atmosphere, the 
pencil, on being brought into contact with 
the moving paper, will rule a straight line. 
This is called the atmospheric line. 

It is now a common practice to connect, 
by means of pipes, both ends of the steam- 
engine cylinder (fitted with a three-way 
cock) ; so that, by one movement of the 
lever of the latter, the indicator can be put 
in communication with either end of the 
cylinder at pleasure, or it may be shut off 
from both, to produce the atmospheric line 
as above described. 

In order to produce a diagram showing 
the action of the steam in the engine cylin- 



71 



der, if the indicator is put in connection 
with one end of the engine cylinder, the 
spring will be compressed by the steam 
pressure under it ; and the amount to which 
the indicator piston rises is a measure of 
the steam pressure. For example, suppose 
that the spring compresses one-sixteenth of 
an inch for every pound on it : then, if the 
steam pressure is forty pounds, the piston 
will rise two and one-half inches. As the 
piston of the engine travels forward on its 
stroke, the steam pressure begins to dimin- 
ish, and becomes less and less liable to 
compress the indicator spring ; and con- 
sequently the indicator piston continually 
falls. In order to register these continu- 
ally varying pressures, the pencil is kept 
in contact with the paper on the drum of 
the indicator ; and, as the engine piston 
moves backwards and forwards, the drum 
of the indicator partially rotates also, back- 
wards and forwards, coincident with that 
of the engine piston. The curved line thus 
traced by the pencil moving vertically up 
and down on the paper (itself moving at 
right angles to the up-and-down movement 



72 



of the pencil) is called an indicator card or 
diagram. It is nothing more than a regis- 
ter of the varying- pressures in the cylinder 
as the piston moves to and fro. 

In order, also, that the diagram shall be 
correct, it is essential, first, that the motion 
of the drum and paper shall coincide exact- 
ly with that of the engine piston ; second, 
that the position of the pencil shall pre- 
cisely indicate the pressure of steam in the 
cylinder. 

The first condition is frequently some- 
what difficult to bring about, because it is 
not only necessary that the beginning and 
end of the motions shall be coincident, but 
that these and all intermediate points shall 
be so. Owing to the irregular motion of 
the engine piston, consequent upon the 
varying angularity of the connecting-rod, 
it is, therefore, generally advisable to con- 
nect the cord in some way to the piston- 
crosshead. If any other point be chosen, 
it must be carefully seen that the motion 
given does not vitiate the diagram. 

As the motion of the parts mentioned ex- 
ceeds in length the motion of the indicator, 



73 



it must be reduced in length by levers of 
such proportions as may be required for 
that purpose. For example, if the stroke 
of the engine is thirty-six inches, and the 
length of the diagram is to be four inches, 
then the lengths of levers are as one is to 
nine; or, if only one lever is used, then the 
indicator motion must be taken from a 
point on the lever sufficiently far from its 
fixed end to obtain the reduced travel re- 
quired. 

Two of the simplest ways of reducing the 
motion are by a swinging lever, with a pin 
working in a slot of an arm secured to the 
crosshead of the engine, and transmitting 
the motion by a cord to the indicator, as 
shown on pp. 74, 75. 

If the indicator and its spring are in 
good order, the pre'ssure given by it may be 
taken as correct, provided the instrument is 
not placed too near, or exactly opposite, a 
steam-port. In the former case, the flow of 
steam past the opening into the indicator 
generally reduces the pressure indicated 
during the admission of the steam ; and, in 
the latter case, the momentum of the steam, 



74 



especially if wet, causes the pencil to give 
jerky and uncertain indications. The cylin- 
der-heads are usually the best position for 
the indicator. 



ft 



L 



Fig. 5. 



V 



\ 



^ 



\ 



\ 



\ 



\ 



\ 



\ 







\ 



\ 



V 




It is advisable to take diagrams from 
both ends of a cylinder, as the two dia- 
grams always differ more or less ; and, in 



7d 



calculating the power, the area of the piston- 
rod must be deducted from the area of that 
side of the piston. 




The indicator should be run for a few 
minutes, so that it may become hot, before 



the diagrams are taken ; and if any part 
works stiffly, this should be rectified. After 
taking the diagram, a note should be made, 
on the back, of the date, name of builder of 
engine, description of engine, diameter of 
cylinder, length of stroke, number of revo- 
lutions, the atmospheric pressure, boiler 
pressure, scale of diagram, and any other 
particulars it is desirable to have on record. 
As I have before stated, the indicator is 
an instrument by means of which a steam- 
engine is caused to write on a piece of 
paper an accurate record of the perform- 
ance that takes place within the cylinder. 
It gives a record which, to the un instructed 
eye, is unintelligible, but by engineers is 
looked upon as the most reliable statement 
they can have of the work done by an en- 
gine, inasmuch as it tells at each and every 
part of the stroke of the piston what are the 
effective pressures tending to produce mo- 
tion, and what are the back pressures tend- 
ing to detract from the effective pressures. 

INDICATOR DIAGRAMS. 

Assuming that we have an indicator at- 



77 



B 



tached to a steam-engine cylinder, and so 
connected that the drum containing the 
paper is moving to and fro coincident to 
the piston of the engine ; before letting in 
steam to the indicator cylinder, if we apply 
the pencil to the surface of the paper, it 

Fig. 7. 



will draw upon the paper a horizontal line, 
VV, in length proportioned to the stroke of 
the engine. (See Fig. 7.) 

Now, if we open the cock attached to the 
indicator cylinder, and assume that the 
engine piston has just commenced to move 
from left to right, the indicator piston will 
also move vertically ; and the pencil will 



78 



trace the line KB, representing the pressure 
per square inch of the steam in the engine 
cylinder. 

Assuming that the indicator spring be 
one which would compress one inch for 
every 40 pounds pressure per square inch 
acting on the piston, then, if there were 100 
pounds pressure per square inch on the en- 
gine piston, the pencil would rise two and 
a half inches from V to B. Now, suppose 
the engine piston to have completed its 
stroke, —the pencil having traced the line 
BC, — and the slide-valve to have opened 
the exhaust-port so as to allow the steam 
to escape : then the indicator piston will 
fall, and the line CV will be traced. On the 
return stroke, the pencil would follow the 
line VV, with the exception of any diver- 
sion caused by steam that might remain in 
the cylinder in consequence of the steam not 
having been perfectly exhausted. Leaving 
this out of the question, it would have re- 
turned to the point V on the right, and 
thence to V on the left, thus describing a 
parallelogram, of which the horizontal line 
VV would represent a proportion of the 



79 

) 

stroke of the piston, and the vertical line 
VB would represent the steam pressure upon 
the pistons. The area of this parallelogram 
would, therefore, represent pounds pressure 
into feet moved through by the piston in 
its stroke, or revolution of the engine. 

Now, for simplicity, suppose that the 
line VV (Fig. 7) represents a foot-stroke 
of the piston of 1 foot, that the piston has 
an area of 99 square inches, and that the 
line VB represents 100 pounds pressure to 
the square inch : then we shall have 100 
pounds multiplied by 1 foot ; and this 
equals 100 foot-pounds, which, multiplied 
by 99 square inches (area), will equal 
9,900 pounds as the work performed by the 
piston in one stroke, or half revolution. 
For both strokes, we have 9,900 multiplied 
by 2, equalling 19,800 pounds, as the force 
exerted by the engine through one revolu- 
tion. If the engine makes 100 revolutions 
per minute, then 19,800 x 100 = 1,980,000 
pounds would be the force exerted by the 
piston of such an engine in one minute. 
This, divided by 33,000, gives 60 horse- 
power, which is called the gross indicated 
horse-power. 



80 



Diagram, Fig. 7, is one that seldom, if 
ever, occurs in practice. When such are 
produced, they are only justified by the 
desire to obtain the greatest possible power 
from a given size of engine, without regard 
to the highest economy. It will be seen 
that steam was supposed to have been 

Fig. 8. 



admitted during the whole length of the 
stroke, and that no advantage whatever 
has been taken of the expansive property 
of the steam. 

Diagram Fig. 8 shows steam used ex- 
pansively. 

Assume the same data as in former case, 



81 



— the 100 pounds pressure above the at- 
mosphere has raised the pencil from V to 
B; also assume that the steam has been 
admitted to the engine cylinder up to the 
point e (half the length of the stroke), and 
then cut off by the valve : the steam now 
in the cylinder begins to expand ; and, as it 
expands, it loses pressure. By the time, 
therefore, that the piston has arrived at O 
from e, the steam will have lost pressure ; 
and the pencil will gradually fall, and trace 
the curved line /. By the time the piston 
has reached the end of the stroke, the 
pressure will further have diminished, say 
to g ; and, when the exhaust opens, it falls 
down to F. 

It will be seen by this diagram, that, 
although only half as much steam was ad- 
mitted into the cylinder as in the case of 
diagram Fig. 7, the area of the diagram is 
very much more than half of that of Fig. 7. 
As a matter of fact, it is about 0.83 of that 
area ; and thus a power 0.83 has been ob- 
tained by using expansively half the steam 
that was required in the case of Fig. 7. 

As a further illustration, Fig. 9 is a dia- 



82 



gram that would be produced if the steam 
were cut off when the piston had moved 
one-fourth of the stroke. In this instance, 
only one-fourth the steam would be re- 
quired as for Fig. 7. But the total area 
of the diagram is about 0.54 of that of 

Fig. 9. 




Fig. 7 ; so that 0.54, or more than one-half 
as much work, is obtained for one- fourth 
of the steam. 

Fig. 10 is a diagram taken from a Corliss 
engine, 8 inches diameter and 24 inches 
stroke, 90 revolutions per minute. 

Starting from the top corner 5, the steam 
pressure remains uniform to about point e; 



83 



here, the cut-off valve being closed, the 
pressure commenced to fall, as represented 
by the curved line /, until it reached the 
point g, when the exhaust-valve being 
opened, allowing the steam to pass into the 
atmosphere, it quite suddenly drops from 

Fig. 10. 
B C 




g to Z), — when the piston begins to return. 
There remains a slight pressure in the 
cylinder until the time the piston gets to 
7i, that is the back- pressure throughout the 
stroke ; so that it keeps the line of the pen- 
cil about 0.6 of a pound above the atmos- 
pheric line AD, until the closing of the 



84 



exhaust- valve, which occurs at the point 7i, 
— after which time the steam remaining in 
the cylinder is compressed, raising the in- 
dicator pencil, and forming the curved line 
hi. 

In this case, the effective work done by 
the engine is represented by the area con- 
tained within the irregular figure, B, e,f, g, 
D, 7^, and i. This is after allowing for the 
back-pressure and the compression, which 
are contained between that figure and the 
lines i, 7i, and D. 

We have now described how a diagram 
is taken from one end of the cylinder. To 
obtain it from the other, all that has to be 
done is to make a pipe connection from the 
three cylinder-heads fitted with a two-way 
cock (as before described); and diagrams 
may be got on the same piece of paper, and 
would, if the engine were perfectly equal in 
performance at the two ends, be repre- 
sented as it was in this case, by the dotted 
line on Fig. 9. The sum of these two areas 
will represent pounds pressure through the 
length of the stroke of the piston in a whole 
revolution, which, multiplied by the area of 



85 



the piston and the number of revolutions 
per minute, will give the foot-pounds. 
This, divided by 33,000, will give the gross 
indicated horse-power of the engine. 



USE OF THE INDICATOR FOR SHOWING THE 
CONDITION OF THE ENGINE. 

The indicator tells us not merely the 
power exerted by the engine, but the nature 

Fig. 11. 




of the faults by which the power is im- 
paired. Thus, the shape of the indicator 
diagram may show that the steam or 
exhaust .ports are too small, or that the 
valve has not sufficient lead, or is improp- 
erly set. Let us take, for example, the 
above diagram, Fig. 11. 

When the indicator pencil is at the point 



86 



J3, the engine piston is at the commence- 
ment of its stroke, the paper drum in mo- 
tion. The line is traced from B to e, and 
thence to g, at which point the stroke is 
finished in this direction. At the point e 
the valve closed the steam-port, or, in other 
words, the steam was cut of! ; and, while 
the line from e to g was being traced, the 
steam pressure in the engine cylinder was 
expanding, and its pressure consequently 
decreasing, as shown by the falling of the 
line /. The line from e to g being convex, 
instead of concave (as per dotted line), 
shows that either the slide-valve or the 
piston, probably both, were not in good 
order, and admitted steam during expan- 
sion. The fall of the steam-line from B to 
e also shows that the steam-ports are too 
small. At the point g the exhaust- valve 
is opened to the atmosphere, the steam 
escapes, the pressure in the engine cylinder 
falls, and the pencil descends towards D. 
The diagram, as here indicated, shows that 
the exhaust-port is opened too late, for this 
corner of the diagram should be very nearly 
square (see dotted line p). The engine 



87 



piston now commences its return stroke, 
and the line gli is traced, representing the 
exhaust-line : and, before reaching the end 
of its stroke, it commences to rise again at 
h, thus indicating that there is some press- 
ure arising from the compression of the 
steam and vapor remaining in the cylinder. 
This is due to the closing of the exhaust- 
port at h before the end of the stroke, 
causing the curved line hi. The rounded 
corner at B shows that the valve is want- 
ing in "lead:" or, in other words, the 
steam-port was opened too late, as is also 
the case at the exhaust-end ; in the latter 
case, showing that the release of the ex- 
haust steam is not early enough, and that 
in consequence of this the back-pressure at 
the commencement of the return stroke is 
much too high. This shows that the slide- 
valve was improperly set, — a defect which 
can be remedied by shifting the eccentric 
slightly ahead. This will improve the ex- 
haust, by causing an earlier opening, shown 
by the dotted curved line g; also causing 
earlier compression, as shown by the dotted 
line at the point of compression, as well as 



88 



the increased lead and initial steam press- 
ure at B. The power exerted is thus in- 
creased at least ten per cent with the same 
amount of steam. The steam-line should 
be parallel with the atmospheric line up to 
point of cut-off, or nearly so. Should it 
fall, as the piston advances, the opening 
for the admission of steam is insufficient, 
and the steam is ivire-drawn. 

The point of eut-ofT on all engines should 
be sharp and well defined ; if otherwise, it 
shows that the valve does not close quick 
enough. 

By having an indicator at each end of the 
engine cylinder, the back-ancl-forth action 
of the steam in the cylinder is simultane- 
ously recorded in the form of a diagram, as 
before stated, by horizontal and vertical 
lines and curves. This diagram comprises 
time of admission, steam-line, point of cut- 
off, expansion curve, terminal pressure, 
point of exhaust (or relief exhaust) line, 
back-pressure line, compression curve, ini- 
tial pressure, and initial expansion. From 
these records the total work clone by the 
steam can be accurately ascertained. Very 



89 



accurate measurements have been made by 
the indicator ; but the average area of indi- 
cator cylinders is only about one-half of a 
square inch, while that of cylinders indi- 
cated may vary from ten square inches to 
as many square feet. By the use of the 
indicator, the determination between nomi- 
nal (calculated), indicated (real), and effec- 
tive horse- power is found, — the variations 
between which are very marked. 

The indicator also furnishes one of the 
data for ascertaining the power exerted by 
the steam-engine ; namely, the mean or 
average pressure of the steam during the 
stroke on each square inch of the piston. 
Stated more accurately, it shows the excess 
of pressure on the steam side of the piston 
to produce motion, over that on the exhaust 
side to resist it ; and from no other source 
can it be so accurately ascertained. 

The pressure in the boiler is readily 
known ; but the steam in its passage to the 
cylinder is subject to various losses, such 
as wire-drawing, condensation, friction, 
etc., so that frequently the pressure on the 
piston does not exceed two-thirds of that 
on the boiler. 



90 



HOW TO ASCERTAIN THE HORSE-POWER OF A 
DIAGRAM. 

A horse-power being 33,000 pounds 
raised one foot high per minute, to ascer- 
tain what an engine is exerting all we need 



Fig. 12. 
E F G 



H 



1 




















t 
1 
1 


t " 


I 

1 
1 

\l 
\l 


1 
1 

1 
1 
1 
1 


1 


5 ! 7 
1 
1 
1 
1 

1 
1 


\ 

45^ 

1 

1 
i 


1 
1 
1 


27 

1 


22 


18 


10 




I 

1 


S&fcL — 


1 
1 
1 
1 
\ 


1 

1 
1, 
I 


1 
1 
1 
i 


1 

1 

1 


1 

1 

1 

1 
J, 


1 

1 
1 

X 


1 \ 



SCALE 1=40 POUNDS 

is to find out how many pounds weight it 
will raise in a minute, and through how 
many feet. The above card we will take 
as an example. 

This diagram has registered on it all 



91 



the lines and pressures heretofore men- 
tioned. 

The connection between this curved fig- 
ure, and the power exerted by the engine, 
is not apparent at first sight ; and, before 
showing how to obtain it, it is necessary 
for the reader to look back to the begin- 
ning of this article, to see what is the true 
measure of power exerted. 

Without a clear and definite conception 
of what constitutes mechanical work, — or, 
in other words, what is the measure of work 
done, — it is impossible to form any idea, 
either of what is meant by economical use 
of steam, or of the connection between the 
indicator diagram and the indicated horse- 
power. 

The simplest example of an expenditure 
of power, and also the most common, is that 
of a weight raised from the ground. If one 
pound has been raised one foot high, just 
half the work has been required which would 
be required to raise two pounds one foot 
high. This is so simple a conception as 
not to require further explanation. A lit- 
tle consideration will show that, generally 



92 



speaking, the work required to lift any 
weight to any height may be said to be 
equal to a certain number of pounds raised 
one foot high ; or, as it is generally stated 
for the sake of shortness, the work ex- 
pended is equal to a certain number of foot- 
pounds. One pound raised one foot is one 
foot-pound. 

It is a well-known law in mechanics, that 
when work is done, or power expended, 
some resistance has been overcome through 
some distance. What is really done in 
raising a weight is to overcome the attrac- 
tion of the earth, or gravity. We make 
gravity a general standard of resistance, 
and whenever any resistance is overcome 
we may refer it to this standard. One 
pound raised one foot high may be taken 
as our standard unit of work done. 

An engine at work overcomes some re- 
sistance, either propelling itself, a vessel, 
pulling a train, or driving machinery ; and 
the amount of work expended by the en- 
gine in overcoming this resistance through 
a certain distance is equivalent to a certain 
number of pounds raised through a certain 
number of feet. 



93 



WHAT AN INDICATOR DIAGRAM SHOWS. 

Let me refer to the indicator diagram, 
Fig. 12, as it came from the indicator. 
This diagram is the result of two move- 
ments ; namely, a vertical movement of the 
pencil proportioned to the steam pressure 
acting on the piston of the indicator, and 
a horizontal movement of the paper simul- 
taneous with the stroke of the engine 
piston. It consequently represents, in its 
length, the stroke of the engine on a 
reduced scale •, and by its height, at any 
given point, the pressure on the engine 
piston at a corresponding point in the 
stroke. The pressure shown is measured 
by a scale marked to correspond with the 
indicator spring used. The most common 
scales are 20, 30, 40, and 60 pounds per 
inch : that is, an inch of vertical height on 
the diagram represents 20, 30, 40, and 60 
pounds of steam per square inch on the 
piston, according to the scale of the spring 
used. These scales are sent with every 
instrument. 

The length of the diagram, measured 
horizontally, represents the space passed 



94 



through by the piston in feet, and is known 
when we are given the length of the engine 
crank. 

As the pressure is given by the indicator 
scale in pounds, the area of the figure repre- 
sents the work in foot-pounds done by the 
steam on one side of the piston in one com- 
plete stroke, or a revolution of the crank. 

The diagram Fig. 12 is divided into ten 
equal spaces. The distance from A to B 
is one-tenth of the whole length of the in- 
dicator card ; and, during the time the drum 
moved horizontally from A to B, the piston 
of the engine travelled one-tenth of its 
stroke ; while the drum travelled from B 
to (7, the piston of the engine moved an- 
other tenth of its stroke ; and, when the 
engine had travelled its whole stroke, the 
drum would have travelled from A to K, 
and similarly on the return stroke. It is 
not a matter of any importance what the 
length, AK, is when compared with the 
stroke of the engine : so, for convenience, 
AK is usually made about four inches. Ex- 
cepting in engines running at high speeds, 
the length is reduced as much as possible 



95 



compatible with accuracy. This is to avoid 
errors caused by shock and jar of changing 
direction of motion of the paper-drum of 
the indicator. All that we care about is, 
that, when the engine piston has moved 
through a portion of its stroke, the drum 
shall have moved with it in reduced pro- 
portions ; and that the motions of both cor- 
respond at all points throughout the stroke. 
Then we have only to look at the indicator 
card to see what pressure of steam there 
was in the cylinder at any part of the 
stroke. In this particular case a -fa spring 
was in the indicator; which means, that, for 
every one pound pressure on the square 
inch of the indicator piston, the pencil of 
the indicator will rise ^ of an inch. 

If we have 80 pounds cylinder press- 
ure, the pencil will rise two inches as soon 
as the steam is admitted at line A; then, as 
the engine and card move, the pencil moves 
to -B, then to (7. Between this point and 
D, the steam is cut off; then the steam 
pressure falls as the piston moves on, and 
the pressure can no longer compress the 
spring the full height : the pencil falls to F, 



96 



then to 6r, and so on to K, where the steam 
is exhausted into the air ; and, the spring 
being no longer compressed, the pencil falls 
to the line called the atmospheric line, — a 
Hue of no pressure, which will be referred 
to hereafter. 

At the bottom of line K the piston begins 
the return stroke, and up to C the steam 
continues to exhaust into the air. At about 
this point the slide-valve closes ; and what 
is left in the cylinder is compressed until 
nearly the top of line A is reached, when 
the slide-valve again opens, and steam is 
admitted for the next stroke, and the spring 
compressed as before to the top of line A. 

From the curved figure thus formed we 
find what power the engine was developing. 
To calculate this area approximately, it is 
usual for engineers to measure the pressure 
at ten places, equally distant from each 
other, on lines drawn between the lines A s 
B, etc. (see dotted lines, Fig. 12). These 
pressures added, and divided by ten (the 
number of spaces), will give the mean effec- 
tive indicated pressure acting on the piston 
during one stroke. 



97 



To find the foot-pounds raised per min- 
ute, we multiply the area of piston by the 
mean pressure, by the revolutions per min- 
ute, and by the stroke multiplied by two. 

To find the horse- power, we divide the 
foot-pounds by 33,000. This quotient is 
the indicated horse-power of the engine ; or 

Area of piston X mean press. X rev. X stroke x 2 
" 33000 

Where there are a number of cards taken 
from the same engine to be calculated, we 
find what is called " the constant " for the 
engine. This constant is the horse-power 
which would be exerted by one pound of 
mean pressure, and is found by multiplying 
the area of the piston by the feet travelled 
by the piston per minute ; that is, multiply- 
ing the area of the piston by the revolutions, 
by the stroke, and by two, and dividing the 
product by 33,000. We find the horse- 
power of this particular engine by multi- 
plying this constant by the mean pressure. 
In illustration of the rules given before, 
we will compute the horse-power exerted 
in the following diagram, taken from the 



98 



cylinder of a Corliss engine. The diameter 
of piston was 6 inches, the length of stroke 
16 inches, and the revolutions per minute 
108 ; diameter of piston-rod, 1^ inches. 

Fig. 13. 




What is the horse-power of this engine by 
the indicator? 

Cylinder, 6 inches ; stroke, 16 inches ; 
revolutions, 108; boiler pressure, 70 pounds; 
To find the mean effective pressure on the 
piston, proceed as follows : — 

Divide the card into ten equal parts, and 
measure the length of each ordinate by the 



99 



scale corresponding to the spring of the in- 
dicator (which, in this case, was 40 pounds 
for each inch in height). The sum of the 
length of the ten ordinates amounts to 344 
pounds, which, divided by the number of 
ordinates (ten in this case), gives an aver- 
age mean effective pressure of 34.4 pounds. 

A horse-power is a conventional term, 
and expresses a rate of mechanical work, 
measured in foot-pounds for some unit of 
time, as one second, or one minute : 550 
pounds raised one foot high in one second, 
or 33,000 pounds in one minute, is common- 
ly understood to mean a horse-power. 

To calculate the indicated horse- power, 
multiply the area of the piston in square 
inches by twice the length of stroke in feet, 
and the products by the number of revolu- 
tions per minute. (This product is known 
as the "piston displacement.") Divide 
this product by 33.000, and the result is the 
41 horse-power constant," or the power de- 
veloped for every pound of mean effective 
pressure. Multiply the quotient by the 
mean effective pressure (ascertained from 
the diagram), and the result will be the 
indicated horse-power. 



100 



.rea of piston = 6 X 6 X 0.7854 



28.274 square inches. 



Area of piston-rod = 



1.5 X 1.5 x 0.7854 



= 0.883. 



Average area of piston less one-half area of rod 
equal 27.391 (28.274 - 0.883 = 27.391), 



Speed of piston in feet per minute 

, 16" x 2X108 
equal — — — 

\4j 



= 288'. 



The constant for this engine is, therefore, 



HP = 



27.391 X 288 



= 0.239 horse-power constant. 



33000 

The mean pressure, as per diagram, is 
34.4 pounds, and the power developed was 

HP - 34.4 X 0.239 = 8.22 horse-power. 

Where great accuracy is required in es- 
timating the power of steam-engines from 
indicator diagrams, care should be taken to 
calculate the power of forward and back 
strokes separately, as the mean effective 
pressures are not always alike. 

In this manner the power exerted by an 
engine may be ascertained under every va- 
riety of circumstances, and also the power 
required for every kind of machine. 

Measuring the power required by a single 



101 



machine, among many running in a manu- 
factory, requires great care, but can be clone 
with certainty, even to a small fraction of 
a horse-power. It is necessary that every 
thing should be in the same condition dur- 
ing the whole experiment. The proper time 
to test is after running for several hours, 
and directly after stopping, when every 
thing is in the best working condition : say 
at noon-time. Then, first indicate for the 
shafting alone ; afterwards put on the ma- 
chine to be tested, — the power required for 
which is to be ascertained after it has been 
running for a few minutes ; and, finally, 
after the belt has been thrown off, indicate 
for the shafting again. 

In case the pencil should run over the 
paper several times, it should be ascertained 
if it follows the diagram exactly when re- 
moved a little from the paper. The first and 
third diagrams (that is, the friction diagram 
of the shafting) should be identical, and the 
excess of the second diagram is the power 
required by the machinery tested. Care 
should be observed that all the diagrams 
are taken at the same speed of the engine. 



102 



In all cases the greatest pains should be 
taken to determine if the diagrams are a 
true representation of the power exerted : 
see if the pencil will repeat the diagram, 
both when in contact and w T hen not in con- 
tact with the paper. Often the diagram 
will not repeat exactly. Whenever this is 
the case, the pencil must be allowed to run 
over the paper a sufficient number of times ; 
and the average of all the figures must be 
taken as the true one. 

As before stated, the indicator card is 
usually run out — or, in other words, the 
mean pressure of the card is usually ascer- 
tained — by reading off, with the aid of the 
scale, the different mean pressures on each 
of the ten spaces, then adding them to- 
gether, and dividing them by ten, or what- 
ever number of spaces there are. This is 
correct, provided each reading is an accu- 
rate one. The following is a far better 
and easier method : Take a long strip of 
paper, say one-half an inch wide, and from 
10 to 20 inches long, according to the na- 
ture of the card ; mark a starting-point on 
the edge near one end ; then lay the strip 



103 



of paper along the first dotted line, and 
mark off the length of that line ; then lay 
it on the second space, and add the length 
to the second dotted line ; and so on to 
the tenth dotted line. By this means, the 
lengths of all the ten lines are laid end to 
end. If we now take a rule, and read off 
how many inches there are in the whole 
length, and divide them by ten, we get the 
number of inches in the mean pressure of 
the whole card. Generally expressed, we 
multiply the total number of inches read 
off the strip, by the scale, and divide by 
ten. This is one of the best and safest 
ways, if not the very best way, of finding 
the mean pressure of a card. It is certainly 
greatly superior to the method of reading 
off ten different pressures, and adding them 
together, and dividing by ten, as heretofore 
described. 

There is another method of measuring 
cards, which at once disposes of many 
vexatious causes of error. It is by a most 
ingenious instrument called a planimeter, 
which is now mostly used for finding mean 
pressures. This instrument is about as 



104 



large and as complicated as a pair of divid- 
ers. It will give the area of any card, 
however awkward in shape, in one minute, 
by passing one leg of the instrument along 
the outline. It gives at once the mean 
effective area, without any second measure- 
ment being required for counter- pressure ; 
or it measures any of the areas of a card 
which may be desired. No skill or mathe- 
matical knowledge whatever is required to 
use the instrument. 

One leg of the instrument is caused to 
remain stationary, and a tracer on the other 
leg is passed along the outline in one direc- 
tion till it returns to the starting-point. 
The readings taken from a counter on the 
instrument give the area of the enclosed 
figure. Marvellous accuracy and perfect 
simplicity are the marked features of the 
planimeter. 

In working out a number of cards with a 
planimeter, it is most important to remem- 
ber that the length of the card must be 
taken into account, because this generally 
varies to a slight extent in cards taken 
from the same engine with the indicator ; 



105 



and it does not do to assume a common 
length for them all. 

HOW TO DIVIDE A LINE INTO A REQUIRED 
NUMBER OF EQUAL SPACES. 

A foot-rule or scale is usually divided 
into inches, halves, quarters, and eighths 
of an inch ; and, when the line to be divided 
into a required number of equal spaces is 
a multiple of those spaces in any of three 
units of measurement, it is, of course, easy 
so to divide it. Thus it is easy, by apply- 
ing the rule, to divide a line four inches 
long into four inch spaces, or eight half- 
mch spaces, or sixteen quarter-inch spaces, 
or thirty-two eighths-of-an-inch spaces. 
But, when the line is not such a multiple of 
the space, it cannot be divided by applying 
the rule to it ; and the following method 
may be used : — 

A line 4| inches long, to be divided into 
10 equal spaces. First draw a line at right 
angles to the given line, at one end of it ; 
then take a strip of paper, and, applying 
the rule to the strip, mark off on it 10 
equal spaces, which together will exceed 



106 



the length of the given line ; then place 
one end of the strip at the open end of 
the given line, and carry the other end of 
the strip up until the last point marked off 
on it touches the right-angled line, and 
through the points on the strip draw lines 

Fig. 14. 




parallel with the right-angled line to the 
given line ; and the given line will be 
divided as required. 

Thus, let AB (Fig. 14) be the given line ; 
draw BD at right angles to it ; the first 10 
equal spaces on the rule which will exceed 
the length of AB (2 T \ or 2.0625) will be 
10 one-quarter inches ; mark these 10 one- 



107 



quarter inches off on a strip, A to D; place 
the end A of the strip to the end A of the 
line, and move up the strip until the point 
D touches BD; and, through points on the 
strip, draw lines 1, 2, 3, 4, 5, 6, 7, 8, and 
9, parallel with BD; and the line will be 
divided into ten equal spaces. 

To those who do not have a planimeter, 
and are frequently in the habit of comput- 
ing the horse-power of engines from indi- 
cator diagrams, this method will be found 
very advantageous. 

A diagram from a condensing, or u low- 
pressure," engine differs from one produced 
by a non-condensing, or u high-pressure," 
engine ; from the fact, that, in the former, 
the line of back-pressure, instead of being 
a little above atmospheric pressure, ap- 
proaches more or less to that of perfect 
vacuum. 

In calculating the power from diagrams 
of condensing, or " low-pressure," engines, 
it is usual to measure the area above and 
below the atmospheric line separately. This 
method gives the value of the average vacu- 
um obtained, and thus indicates the extent 



108 



to which the back- pressure is reduced below 
atmospheric pressure. (See diagram Fig. 
15.) 

In this the average mean pressure due to 
the steam was 

21 + 21 + 6 = 48 lbs., 

which, divided by 10 (the number of divis- 

Fig. 15. 

B — C 



u 


& 
















2 


l 2 


1 \ 6 • o • t 


> 1 o i 


o 


• O t <o * b 






r 


X 






i - D 


1 


2 1 


2 1 


2 1 

1 


1 9 

i_ ^ 


>^4_ 


5. 


5 


4.5 4 2.5i 


:; ,zi> 



ions on the card), equals 4.8 pounds ; and 
the average vacuum realized was 

12+12+12+11+9+6.5+5+4.5+4+2.5=78.5 lbs., 

which, divided by 10, equals 7.85 pounds: 
showing that the power realized in this case 
by removing the resistance of atmosphere 



109 



was about sixty per cent of that shown by 

the indicator ; thus, — 

7.85 - 4.8 „ 

— — == 60 per cent. 

4.8 ^ 

In well-constructed engines, with an early 
cut-off, the expansion curve eg (diagram 
Fig. 15) will often cross the atmospheric line 
AD before the piston has moved half the 
length of the cylinder. In such cases as 
this, the mean pressure represented by the 
area above the atmospheric line AD will be 
less than below it, which difference is due 
to the reduced back-pressure by reason of 
the comparative vacuum in the condenser. 
The above diagram, Fig. 15, indicates a 
large amount of expansion. 

INDICATED HORSE-POWER. 

The indicated horse-power is the power 
developed by the steam on the piston of the 
engine, without any deduction for friction. 
The indicated horse-power is calculated 
from the diagram or cards taken by the 
application of the indicator to the steam- 
engine cylinder. It is the total unbalanced 
power of an engine employed in overcoming 



110 



the combined resistance of friction and the 
load. 

EFFECTIVE HORSE-POWER. 

The effective horse-poiver is the actual and 
available horse-power delivered to the belt 
or gearing, and is always less than the in* 
dicated, from the fact that the engine itself 
absorbs power by the friction of its moving 
parts. 

ENGINE FRICTION. 

The power absorbed in driving an engine 
against its own friction is a most variable 
quantity. With a good and well-constructed 
engine, having ample bearing surfaces, effi- 
cient means of lubricating them, and valves 
nearly balanced without over-complication, 
the friction may not exceed ten per cent of 
the indicated power ; but in badly con- 
structed engines the friction may be nearer 
fifty per cent. In the case of an engine 
having ordinary unbalanced slide-valves, it 
is probable that quite one-third of the whole 
frictional resistance is due to the valve. 
The heat due to the internal engine friction 



Ill 



— that is to say, the friction of the valves 
and piston — is imparted to the steam ; and 
either the whole or greater part of it is 
carried to the condenser or atmosphere 
with the exhaust steam. 

The power absorbed in overcoming fric- 
tion is not only wasted, but it is wasted in 
wearing out the engine. 

In the diagram, Fig. 13, the calculation 
gave what is called the indicated power ; 
that is, the effective available power of the 
engine. It does not show the gross or 
whole power of the engine. This gross 
power is reduced to effective motive power 
in three ways ; namely : — 

First. In expelling the steam left in the 
cylinder at the end of the stroke ; the ex- 
pelled steam carrying its heat with it to the 
atmosphere in a non-condensing, or tk high- 
pressure," engine, and to the condenser in a 
condensing, or " low-pressure," engine. 

Second, In compressing the steam in the 
cylinder after the exhaust-port is closed ; 
but, as this steam is again used after com- 
pression, the power used in compressing it 
is not necessarily wholly wasted. 



112 



Third, In overcoming the friction of the 
moving parts of the machinery ; including, 
in locomotives, the friction on rails, and, in 
stationary engines, the friction of the belt 
or gearing. 

The effective available motive power will 
therefore vary in proportion to the power 
lost through these reducing causes. The 
less power required to expel and compress 
the steam left in the cylinder, and to over- 
come the friction, the greater will be the 
effective motive power ; and vice versa. 

In calculating this power, however, from 
a diagram, only the first and second of these 
causes are or can be considered. 

The piston of an engine is always acted 
upon by two opposing forces, — one propel- 
ling and the other repelling ; and the dif- 
ference between them is what, in practice, is 
called the effective motive force or power. 

The propelling force must, of course, in 
all cases, be sufficient at least to overcome 
the repelling force, or back-pressure. This 
back-pressure, as will presently be seen, is 
always greater in non-condensing, or " high- 
pressure," engines than in condensing, or 



113 



" low-pressure/' engines. In the former, 
the propelling steam left in the cylinder at 
the end of the stroke — that is, the exhaust 
steam — escapes, or is expelled into the air : 
in the latter, into the condenser. In the 
former, the back-pressure must necessarily 
be at least the pressure of the atmosphere, 
which averages about 14 pounds to the 
square inch ; but it is always greater than 
this, because of the friction of the exhaust 
steam in the ports and pipe connections ; 
and in badly constructed engines it is much 
greater. In condensing, or ; 4 low-pressure/ ' 
engines, the back-pressure should always 
be less than the pressure of the atmosphere, 
depending upon the approximation to vacu- 
um obtained in the condenser. 

In the diagram, Fig. 16, taken from a 
non-condensing engine, it will be seen that 
the back- pressure line gdh is considerably 
above the atmospheric line AD, and indi- 
cating excessive back-pressure. 

Excessive back-pressure in a non-con- 
densing engine is caused by or results from 
too great impediment to the escape of the 
exhaust steam ; and, in condensing engines, 



114 



to imperfect vacuum in the condenser. The 
value of the indicator in revealing defects 
of this kind cannot be over-estimated. 



B 



Fig. 16. 




The difference between a non-condensing 
and a condensing engine is, as has been 
seen, that in the former the exhaust steam 
escapes or is expelled, more or less directly, 



115 



according to the construction of the port- 
passages and pipe connections, into the air ; 
and, in the latter, into the condenser. 

In the former, the back-pressure is the 
pressure of the atmosphere, increased more 
or less as the escape of the exhaust steam 
is more or less impeded. In the latter, 
the back-pressure depends chiefly upon the 
pressure of the exhaust steam, or, in other 
words, the degree of vacuum in the con- 
denser. 

The condenser is an air-tight iron box or 
vessel, fitted with valves, and connected 
more or less directly by pipes with the ex- 
haust-ports of the cylinder. Its office is to 
condense the exhaust steam, and thus pre- 
vent the back-pressure of the atmosphere. 
The condensation of the steam is usually 
effected either by bringing it into contact 
with a jet of cold water, or by passing it 
through or about a series of tubes on the 
other side of which cold water is circulated. 
In either case the steam is condensed almost 
instantly ; and a vacuum, more or less per- 
fect, is formed in the condenser. A perfect 
vacuum cannot, in practice, be had ; but an 



116 



average of about 26 inches, or 13 pounds, 
is usually obtained by the gage. Diagrams 
generally show from 3 to 4 pounds less. 
The approximation to a vacuum, and corre- 
sponding diminution of back-pressure, are 
affected in three ways ; namely, — 

First, The temperature of the condensing 
water. 

Second^ The pressure of the atmosphere. 

Third) The friction of the exhaust pipes 
and ports. 

First) If the temperature should be 32° 
Fah., the pressure would be only 0.085 
pounds to the square inch, and the vacuum 
as nearly perfect as is obtainable. The con- 
densing water is, however, usually taken at 
40° to 80°, and leaves the condenser at from 
90° to 120° ; making the temperature in 
the condenser generally about 100°, which 
would give a back-pressure from this cause 
alone, of about one pound to the square 
inch. 

Second, If the barometer stands at only 
28 inches, 13.7 pounds would be a perfect 
vacuum, 30 inches of mercury being equiva- 
lent to 14.7 pounds; and, if the water in 



117 



the condenser be at a temperature of 130 , 
its vapor will form a resistance of 2.21 
pounds : therefore, the lowest attainable 
vacuum would be but 13.7 - 2.21 = 11.49 
pounds. Whereas, if the barometer stood 
at 31 inches, a perfect vacuum would be 
15.2 ; and, if the water was but 100°, its 
vapor would give a resistance of only 0.9 
pounds : and consequently the highest at- 
tainable vacuum would be 15.2 — 0.9 = 14.3 
pounds, making a difference of 2.81, or a 
gain of twenty per cent. 

Third, The friction of the exhaust pipe 
and ports will be excessive, if they are too 
small, to the same extent as in the case of 
non-condensing engines. 

The water used for steam-engine pur- 
poses invariably contains more or less air, 
which, if allowed to accumulate, would 
gradually destroy the required vacuum. It 
is necessary, therefore, to draw off this air 
as well as the water, and this is done by 
means of an " air-pump" worked by the 
engine ; and, of course, the power required 
to do this, although needfully expended, is 
so much power to be deducted from the 



118 



given power, reducing the efficient motive 
power of the engine. The power thus 
expended is usually equivalent to from one- 
half to one pound pressure. But it is fre- 
quently necessary to raise the condensing 
water from a lower level to the line of the 
condenser ; and in that case the power re- 
quired to do this work is also power to be 
deducted from the gross power, also redu- 
cing the efficient motive power of the engine. 
In all cases it is only the net motive power, 
after deducting the power needed to over- 
come the back-pressure, that is represented 
in the area of the diagram. 

The pressure of the atmosphere is usually 
taken as 15 pounds, which is too high, being 
correct only when the barometer stands at 
30.54 inches, — a most unusual occurrence. 
But the error is unimportant, and it is very 
convenient to avoid the use of a fraction. 

The principal object of knowing the ex- 
act pressure of the atmosphere is to ascer- 
tain the duty performed by the condenser 
and the air-pump. The temperature of dis- 
charge being known, the pressure of vapor 
inseparable from that temperature is also 



119 



known (see Nystrom's " Pocket Book," p. 
400) ; and, this being deducted from the 
actual pressure of the atmosphere, the re- 
mainder is the vacuum in which the water 
would boil. The power of the air-pump is 
shown in the closeness with which the vacu- 
um approaches this point. 

The vacuum shown by the indicator will 
generally vary from that shown by the 
vacuum gage when it is constructed with a 
glass tube hermetically sealed at the top ; 
for such gages are designed to show the 
variation from a perfect vacuum without 
reference to the weight of the atmosphere : 
but the vacuum shown by an indicator is 
affected by all its variations. 

AN IDEAL DIAGRAM SHOWING THE ACTION 
OF STEAM. 

Some of the disturbing causes on dia- 
grams of steam-engines, which make the 
real differ from the ideal form of the dia- 
gram, have already been considered inci- 
dentally. At present, the more important 
and usual of these deviations are to be 
classed and considered in detail. 



120 



These causes affect the power of the 
engine, as well as the character and shape 
of the diagram. 

The indicator diagram is, of course, the 
key to the action of the steam in the cylin- 
der. A part of the work performed by the 
steam is spent in overcoming the friction 
of the engine itself ; and, consequently, the 
efficiency of the engine is most fairly tested 
by the amount of external work absolutely 
performed against a brake, or otherwise. 

Where the efficiency of the steam alone 
is concerned, however, the diagram is the 
only true criterion ; and it will be necessary 
to deal with its theory carefully to prevent 
misunderstandings, which are frequent in 
practice. 

THE ACTION OP STEAM IN THE CYLINDER. 

The action of steam in any steam-engine 
cylinder is best understood from a diagram 
representing the varying pressures and vol- 
umes through the stroke. 

Such a diagram is usually obtained by an 
indicator applied to the cylinder, and in 
such case the pressures shown are actually 



121 



B 



those of the steam in use. For purposes of 
comparison and calculation, however, it is 
more convenient to construct an ideal dia- 
gram, as nearly as possible such as would 

Fig. 17. 











c, 




K 


6\ 






i 








! \ 






^^Tn 1 ^ 


m 

1 






f 


i 

i 






Jl_ 


aA 


7 


i 






W 



be given by an indicator applied to an 
engine as nearly perfect as practicable, 
working under the same conditions. Such 
a diagram is shown at Fig. 17, where 
horizontal distances represent volume, and 
vertical distance pressure. 



122 



The several lines on the ideal diagram 
will be designated here, reference being had 
to this diagram. 

The base-lines of the theoretical diagrams 
are as follows : — 

THE ATMOSPHERIC LINE. 

When the atmosphere has free access to 
both sides of the piston of the indicator 
before steam is admitted, a straight line, 
AD, will be drawn by applying the pencil 
to the moving paper. This line is called 
the line of atmospheric pressure, or zero, 
on the steam-gage. From this line we 
measure pressure for non-condensing, or 
u high-pressure,' ' engines. 

THE LINE OF PERFECT VACUUM. 

The line VV represents it. This line 
cannot be drawn by the indicator, but must 
be drawn by hand, parallel with the atmos- 
pheric line, and at the proper distance 
below it, to represent the pressure of the 
atmosphere as shown by the barometer, 
according to the scale of the indicator 
diagram. When the actual pressure is not 



123 



known, it is to be assumed at 14.7 pounds 
on the square inch, corresponding almost 
exactly with 30 inches of mercury, which 
is about the average pressure at the level 
of the sea. The barometric column falls 
y^o of its height for every 262 feet of ele- 
vation above the sea-level. 

THE LINE OF BOILER PRESSURE. 

This line is represented by the letters 
BC, and is also drawn by hand, parallel 
with the atmospheric line, and at the proper 
distance above it, to indicate the steam 
pressure per square inch, as shown by a 
correct steam-gage, measured off by the 
scale of the indicator diagram. It can be 
drawn by the indicator attached to the 
cylinder, only when the engine is at rest, 
and while an equilibrium of pressure is es- 
tablished between the boiler and cylinder. 
It is generally somewhat higher than the 
initial pressure in the cylinder. 

THE CLEARANCE LINE. 

This line is represented by BV, and is at 
right angles to the atmospheric line AD, 



124 



and at such distance from Jcimn that the 
included space, BAV and nmik, correctly 
represents the clearance. 

This clearance is the cubical contents of 
the steam-port passages and the space be- 
tween the piston and the end of the cylin- 
der, or head, to which it is nearest at the 
end or beginning of a stroke. Suppos- 
ing them, when added together, to be at 
each end one-twelfth of the whole cubical 
contents of the cylinder for one stroke of 
the piston, then the distance Am would be 
made one-twelfth {^) of mD. In the dia- 
gram, Fig. 16, one-twentieth (^) has been 
taken, so that the line Am is one- twentieth 
(to) °f the length of mD. It is necessary 
to take these cubical contents into account, 
for the passages and clearance must always 
be filled with steam at each stroke, which is 
compressed and expands just precisely the 
same as the rest of the steam in the cylin- 
der does after the steam has been cut off. 
It is necessary to draw this line, and to add 
this space to the indicator diagram, when- 
ever the theoretical curve is constructed to 
compare with the actual curve traced by 



125 



the indicator, and must be reckoned as part 
of the diagram in calculating the average 
pressure, and in producing the theoretic 
curve, or line of perfect expansion. The 
clearance is, however, rarely given ; and 
it varies in different engines from 1 to 20 
per cent of the space swept through by 
the piston in one stroke. If we have the 
drawings of the engine, we can calculate 
it ; if we know the style of engine, we can 
approximate it. 

The best method, providing the piston is 
tight, is as follows : — 

Put the engine on the centre, remove the 
valve-chest cover, uncover the steam-port 
on the end where the piston is, fill the steam 
passage and piston clearance with water, 
level with the valve-seat ; allow it to re- 
main a few minutes, and, if it maintains its 
level, it is evident the piston is tight : then 
draw off the water, measure or weigh it, 
reduce it to cubic inches, and we have it 
exactly. The number of cubic inches of 
clearance, divided by the cubic inches of 
space swept through by the piston in one 
stroke, gives the ratio of cylinder capacity 



126 



to clearance. This matter will be more 
fully illustrated hereafter. 

DIVISION OF THE OUTLINE DRAWN BY THE 
INSTRUMENT DURING A REVOLUTION OF 

THE ENGINE. 

The diagram, Fig* 17, shows all the lines 
that would be traced by the pencil of the 
indicator during one revolution of the en- 
gine, assuming the action of the steam to 
be nearly theoretically correct. In order 
that the student may better understand the 
subject-matter, the following names have 
been given to the lines represented, as 
follows : — 

The line from i to ft, the admission line. 
The line from k to e, the steam line. 
The line from e to /, the expansion line. 
The line from/ to cZ, the exhaust line. 
The line from d to 7i, the back-pressure, or 

line of counter-pressure. 
The line from h to i, the compression and 

lead line. 

Of these divisions the first four are drawn 
during the forward stroke of the piston, and 



127 



until it is at, or very close to, the termina- 
tion of its stroke ; and the last two are 
drawn during the return stroke. 

ADMISSION LINE. 

The admission line ik shows the rise of 
pressure due to the admission of steam to 
the cylinder. This line is generally very 
nearly vertical ; and, when this is the case, 
it shows that steam of nearly boiler press- 
ure is had at the commencement of the 
stroke, while the piston is nearly stationary. 
Should this line incline forward, as shown 
at B in Fig. 11, or, as at k in Fig. 16, curve 
with the steam line, the reverse is indicated ; 
or should this line continue vertically be- 
yond, and then suddenly drop to the level 
of the steam line, it signifies that the steam 
is wire-drawn, and cannot keep up the full 
pressure as the piston starts forward : but 
should this line, after projecting above, be 
suddenly depressed below the level of the 
steam line, vibrating back and forth one or 
more times on the latter line with acute 
angles of return, it may be attributed to the 
momentum of the reciprocating parts of the 



128 



indicator while running at very high speeds. 
This will be hereafter more fully explained. 

THE STEAM LINE. 

The steam line ke is traced while the 
steam is being admitted to the cylinder, and 
should be nearly parallel to BC, and is in- 
variably several pounds pressure below it ; 
this loss in pressure occurs from radiation 
and friction in the pipes from the boiler to 
the cylinder. This line also represents the 
initial pressure acting on the piston up to 
the point of cut-off, and should be of un- 
varying height, to show that full boiler 
pressure is maintained. It also shows, at 
its termination, the point at which the valve 
closes, or steam is cut off. 

To maintain a proper steam pressure in 
the cylinder, depends, of course, in the first 
place, upon the amount of steam-port area. 
It will be noticed in diagram Fig. 10, taken 
from a Corliss engine, that the piston ob- 
tained nearly the full boiler pressure at the 
very commencement of the stroke. The 
initial cylinder pressure was 97 per cent of 
the pressure in the boiler ; while in the 



129 



diagram Fig. 16 (fitted with the ordinary 
slide-valve, and the steam controlled or 
regulated by a valve in the steam-pipe), 
the maximum cylinder pressure reached but 
88 per cent of the boiler pressure, notwith- 
standing the slower speed of the engine, 
— the former making 90 and the latter but 
40 revolutions per minute. 

An important consideration in connection 
with the admission of steam is that the 
maximum cylinder pressure be fully main- 
tained until the closing of the valve ; in 
other words, that the steam-line traced by 
the indicator should, as much as possible, 
run in a horizontal direction. (See dia- 
grams, Figs. 10, 12, 15, and 17.) To effect 
this it is necessary to have the steam -port 
fully uncovered early in the stroke, so that 
the steam can be rapidly introduced into 
the cylinder. Referring to the above-men- 
tioned diagrams, we find that the steam- 
line is kept well up to the boiler pressure, 
and this pressure is nearly fully maintained 
until the point of cut-off is reached. If we 
take into consideration the small amount of 
lead obtained in these cases, we must at- 



130 



tribute the comparative good results solely 
to the employment of Corliss and Buckeye 
valves, which permit, with a smaller amount 
of angular advance of the eccentric, a very 
rapid and good introduction of steam. 

In locomotive engines the diagrams taken 
with a high rate of expansion, more particu- 
larly at high speeds, the steam-line gener- 
ally falls more or less during the period of 
admission, indicating that the steam-port 
opening is too small. 

THE POINT OF CUT-OFF. 

This takes place at e. In the theoretical 
diagram the corner is abrupt, but in prac- 
tice it is more or less rounded. The dia- 
gram does not always show clearly the 
exact point where the convex curve of 
the rounded corner changes to the concave 
curve of the expansion line ; but the point 
of cut-off is properly located at the point 
where the direction of curvature changes 
from convex to concave. 

THE EXPANSION CURVE. 

This is represented by the line efg, and 



131 



results from a fall of pressure due to the 
expansion of the steam remaining in the 
cylinder after eut-off takes place. The 
actual curve, as drawn by the indicator, will 
be above the theoretical curve laid down 
by the law of Boyle, and Mariotte's law : 
that is to say, the pressure is inversely as 
the volume ; and the curve which expresses 
the pressure for every point of the stroke is 
an equilateral hyperbole. In all indicator 
diagrams a material difference will be no- 
ticed between the true ratio of expansion and 
the corresponding pressures ; the amount of 
departure of the actual pressures from the 
theoretical curve bearing, however, a cer- 
tain relation to the degree of expansion, as 
will be seen hereafter. 

There are various causes which produce 
this action during the period of expansion, 
but their precise influence is more or less 
difficult to ascertain. In the first place, 
leakage at the valves or past the piston is, 
of course, calculated to alter the actual ex- 
pansion curve. 

The effect of leakage, if such occurs, is 
generally easily detected by the irregular 



132 



form of the indicator curves. The main 
cause of the peculiar action of the expand- 
ing steam is, according to a large number 
of experiments made, the heat given off by 
the cylinder to the contained , steam after 
its communication with the boiler has been 
cut off. This condition is facilitated by 
the presence of a certain quantity of water, 
which, at the commencement of the expan- 
sion, has the temperature of the live steam ; 
but, as the pressure is reduced in the cylin- 
der, this water will be instantaneously evap- 
orated, and thus abstract from the cylinder 
a certain amount of heat. The heat ab- 
sorbed with such rapidity is sufficient to 
raise the pressure considerably above that 
which would have existed had no condensa- 
tion and re- evaporation taken place. The 
amount of heat which can be absorbed 
depends, of course, upon the difference of- 
temperature between the steam and the 
metal. 

On the other hand, the mean temperature 
of the cylinder is influenced by the amount 
of protection against radiation and con- 
duction of heat from the cylinder, by the 



133 



amount of c ' throttling ' ' from the boiler to 
the cylinder, by the extent to which expan- 
sion has been carried, and by the speed in 
revolutions per minute. 

When the communication between the 
boiler and the piston is open, the cylinder 
will acquire a temperature practically the 
same as that of the boiler pressure ; and, if 
the cylinder contained nothing but dry or 
superheated steam, this temperature would 
probably be maintained for the greater part 
of the stroke. But owing to a certain 
amount of water which has been deposited 
in the cylinder, and which is re-evaporated 
at the expense of heat imparted to the 
cylinder, this latter will become materially 
cooled by the time the piston has reached 
the end of the stroke. 

From these considerations, the relative 
effect of the various degrees of expansion 
and of speed will readily be appreciated. 
As the degree of expansion is increased, the 
quantity of water converted into steam be- 
comes also greater, — necessitating, how- 
ever, a larger condensation of high-pressure 
steam during admission, — and the longer 



134 



the duration of the stroke. In other words, 
the slower the engine is running, the more 
heat will be absorbed from the cylinder by 
the conversion of this water into steam. 

THE POINT OF RELEASE, OR OPENING, OF THE 
EXHAUST-PORT. 

This is at /, diagram Fig. 17. To pro- 
vide a rapid egress for the exhaust steam, 
and in order that its pressure may be as 
nearly as possible at a minimum, after the 
work in the cylinder has been performed, it 
is necessary that the exhaust-port should be 
opened before the piston reaches the end 
of its stroke. The proper amount of this 
pre-release depends, of course, upon the 
velocity of the piston, and the quantity of 
steam to be discharged, or the grade of 
expansion. If, on the contrary, the steam 
be confined until the last instant, the back- 
pressure at the commencement of the re- 
turn stroke will be considerably increased, 
or in proportion to the period of admission. 
The deficiency of early release produces in 
the indicator curves a sharp corner at g at 
the end of the stroke, as shown in diagrams, 



135 



Figs. 13 and 15. It will be noticed, also, 
that a considerable loss of effective pressure 
is caused for the same reason, as clearly 
shown by the reduction of the area of the 
indicator diagrams. The amount of back- 
pressure against the piston during the 
remainder of the exhaust also depends di- 
rectly upon the amount of release, and in- 
directly upon the speed of the engine. If 
the exhaust-port is not well open at the end 
of the stroke, it is evident that the greater 
volume of the steam must be discharged 
during the return stroke of the piston, until 
the closing of the exhaust-port ; but, as the 
piston attains its maximum velocity at half 
stroke, the minimum back-pressure above 
the atmospheric line must then be greater 
than it would be under the more favorable 
condition of premature escape of the steam. 
Therefore, the non-release of the steam 
before the end of the stroke involves not 
only a direct loss of the work done by the 
steam, as shown by the corner cut off from 
the indicator diagrams, Figs. 13 and 15, but 
its injurious effect is also manifest during 
the greater part of the return stroke. 



136 



The loss of work done through an early 
release of the exhaust is more than regained 
during the return stroke, the back-pressure 
against the piston becoming reduced to that 
of the atmosphere in non-condensing en- 
gines. (See diagram Fig. 13.) 

THE EXHAUST-LINE. 

It is, of course, desirable that the press- 
ure of the steam be got rid of as completely 
as possible before the piston commences its 
return stroke. This is accomplished by 
having the exhaust port and passages suffi- 
ciently large, and opening the port a suf- 
ficient time before the termination of the 
stroke, according to the density of the 
steam to be released, and the velocity of 
the piston. 

The exhaust-line commences at the point 
of release /, Fig. 17, where the expansion 
curve changes to convex as the pencil 
travels to the line of counter-pressure, and 
shows the fall of pressure caused by the 
release or opening of the exhaust-port for 
the escape of the steam before the forward 
stroke is finished, in order to diminish the 



137 



back-pressure. In an engine in which there 
is no pre-release (the exhaust-port opening 
exactly at the end of the forward stroke) , 
the diagram during the return stroke is 
usually a curve more or less similar to the 
line gd. (See Fig. 16.) 

The lower side of the theoretical diagram. 
Fig. 17, used in calculations, being the line 
VV, represents the pressure in the con- 
denser ; or, in non-condensing, or " high- 
pressure," engines, the atmospheric press- 
ure line AD. 

By making the release occur early enough 
(for example, at the point corresponding to 
/, in diagram Fig. 17), the entire fall of 
pressure may be made to take place towards 
the end of the forward stroke, so as to make 
the back-pressure coincide sensibly with 
that corresponding to the line VV. Then 
the end of the diagram will assume a figure 
represented by the line fDd in diagram, 
Fig. 17, which is usually more or less con- 
cave. The greatest amount of work is in- 
sured by making the release take place at 
point/; so that about one-half of the fall 
of pressure shall take place at the end of 



138 



the forward stroke, from / to D, and the 
other half at the commencement of the re- 
turn stroke, as indicated by the curve Dd. 
The line fDd is traced while the excess of 
pressure remaining at the point of exhaust 
is being released. 

BACK PRESSURE, OR LINE OF COUNTER- 
PRESSURE. 

If the steam used in working engines 
were unmixed with air, and if it could es- 
cape without resistance, and in an inappre- 
ciably short time, from the cylinder after 
having completed the stroke, the back- 
pressure would be simply, in non-condens- 
ing engines (called high-pressure engines) , 
the atmospheric pressure for the time ; and, 
in condensing engines, the pressure corre- 
sponding to the temperature in the con- 
denser, which may be called the pressure 
of condensation. The mean back-pressure, 
however, always exceeds the pressure of 
condensation, and sometimes in a consider- 
able proportion. One reason for this, which 
operates in condensing engines only, is the 
presence of air mixed with the steam, which 



139 



causes the pressure in the condenser, and 
consequently the back-pressure also, to be 
greater than the pressure of condensation 
of the steam. For example, an ordinary 
temperature in a condenser when worked 
properly is about 100° Fan., to which the 
corresponding pressure (absolute) of steam 
is about one pound on the square inch ; but 
the absolute pressure in the best condensers 
is scarcely ever less than two pounds on 
the square inch, or nearly double the press- 
ure of condensation. 

The principal cause, however, of in- 
creased back-pressure, is resistance to the 
escape of the steam from the cylinder, by 
which, in condensing engines, the mean 
back-pressure is caused to be from one to 
three pounds on the square inch greater 
than the pressure in the condenser. 

In non-condensing engines, experiments 
show that the excess of the back-pressure 
above the atmospheric pressure varies near- 
ly : As the square of the speed. This ex- 
cess of back-pressure is less, the shorter 
the cut-off is ; in other words, the greater 
the ratio or grade of expansion : that is 



140 



to say, the longer the time during which 
the expansion of the steam lasts. In 
cylinders with a mean of 16 per cent of 
release (that is, with the exhaust-port 
opened when the piston had performed 
0.84 of its stroke), with steam cut off at 
one-half the length of stroke (that is, 

Fig. 18. 
B 




with a ratio or grade of expansion of 2 
nearly) , and with a piston speed of 600 feet 
per minute, being the maximum of speed 
in a good engine, — the excess of the back- 
pressure above atmospheric pressure w T as 
about 0.163 of the excess of the pressure 



141 



of the steam at the instant of release above 
the atmospheric pressure. When the press- 
ure falls during expansion, as in Fig. 18, 
as low as the return or back pressure, this 
exhaust-line does not exist. 

When the steam is exhausted below the 
return pressure, as in Fig. 19, and the ex- 
Fig. 19. 




haust-line is forced up from x to /, it indi- 
cates a rush of steam from the exhaust- 
chamber back into the cylinder. This shows 
that the engine is too large for the work, 
and is working at a loss. 

When the steam is exhausted at a high 
pressure and through cramped passages, 



V 



142 



the exhaust-line extends over most of the 
return stroke, as shown in Fig. 16. 

THE BACK-PRESSURE LINE. 

This is represented by the line clh, and is 
the pressure behind the piston during the 
return stroke, and is called back-pressure 
because it acts in opposition to the return 
movement of the piston. In diagrams from 
non-condensing engines (commonly called 
" high-pressure " engines), it is coincident 
either with one or more pounds pressure 
above the atmospheric line (see diagrams, 
Figs. 13 and 18) ; while in diagrams 
from condensing engines (commonly called 
" low-pressure" engines), it is 22 or 24 
inches of vacuum below, or such a distance 
below the atmospheric line as will coincide 
with the vacuum attained in the condenser 
(see diagrams, Figs. 15 and 17). The 
resistance offered to the escape of the re- 
leased steam has the effect of reducing, by 
a corresponding extent, the effective or 
indicated power of the engine. When the 
steam escapes from a non-condensing en- 
gine, the back-pressure cannot be less than 



143 



the atmospheric pressure (14.7 pounds) at 
the time ; and, when it escapes from a 
condensing engine into a condenser, the 
back-pressure upon the piston cannot be 
less than the pressure of vapor existing in 
the condenser. The excess of resistance 
over these limits depends chiefly upon the 
state of the steam, the size and direction 
of the exhaust-passages, and the speed of 
the engine. Therefore, the passages and 
pipes communicating with the atmosphere 
should be at least fifty per cent larger than 
the ports, and as free from angles as pos- 
sible. 

These requirements apply to condensing 
engines even more strongly ; and, in addi- 
tion, the condenser and air-pump must be 
able to maintain a proper vacuum. 

THE POINT OF EXHAUST CLOSURE. 

This is represented at h in diagram Fig. 
17, and is where the exhaust-port is closed 
against the escaping steam. It cannot be 
located in all cases very exactly by inspec- 
tion ; for while, like the point of cut-off and 
exhaust, it is anticipated by a change of 



144 



pressure clue to a more or less gradual 
closing of the valve, it is not marked by a 
change in curvature of the line. 



THE LINE OF COMPRESSION, OR CUSHIONING. 

This line, when it exists, is formed by 
closing the exhaust before the end of the 



Fig. 20, 




return stroke : for example, at the point cor- 
responding to h on diagrams, Figs. 16, 19, 
and 20. A certain quantity of steam in the 
cylinder is then compressed by the piston 
during the remainder of the return stroke, 
and the rise of its pressure is represented 



B- 



145 



by the curve Jik. In the reduced diagram, 
Fig. 20, taken from one of the most ad- 
vanced types of engines, this curve termi- 
nates at ft, and represents the most advan- 
tageous adjustment of compression, which 
takes place when the quantity of confined, 

Fig. 21. 




v- 



or cushioned, steam is just sufficient to Jill 
the clearance at the initial pressure. 

If this line should be projected above the 
initial pressure, and then suddenly drop 
nearly perpendicular to the level of the 
steam line, thus forming a loop (see Fig. 



146 



21), it would indicate an excess of com- 
pression, due to closing the exhaust too 
soon. It is evident that this would be very 
objectionable, involving a loss of efficiency. 
In computing such a diagram, the area con- 
tained in the loop a?, at the commencement 
of the stroke, — denoting negative work, as 
it were, — should be subtracted from the 
total area included in the indicator diagram. 
Compression also has a useful effect in 
the working of an engine, by providing an 
elastic cushion whereby the momentum of 
the piston and its connections is gradually 
absorbed, and the direction of motion re- 
versed without " thump" or " shock." 
There is no " jar " from the entering steam 
when a new stroke begins. The proper 
regulation of compression serves to make 
an engine work easily and smoothly, and 
consequently reduces the wear and tear of 
the working parts. The pressure due to the 
momentum of these parts will, of course, 
depend upon their weight and velocity in- 
creasing directly as the square of the speed. 
These data being given, the amount of 
cushion, or pressure, required to counter- 



147 



balance work stored up in the reciprocating 
parts can easily be ascertained. It follows 
that the compression should decrease rapid- 
ly as the speed diminishes, and vice versa. 

In fast-running engines, especially loco- 
motives, compression also serves to prevent 
waste from clearance. The capacities of 
the clearance spaces and the steam-ports 
are relatively larger than in most other 
steam-engines, on account of the higher 
speed of the former. These spaces must be 
filled, at the commencement of the stroke, 
with high-pressure steam, which is obtained 
either by taking a supply of live steam from 
the boiler, or by compressing into the clear- 
ance spaces the low-pressure steam that re- 
mains in the cylinder at the closing of the 
exhaust-port. But in the latter process a 
certain quantity of steam is saved at the 
expense of increased back-pressure. It 
should be borne in mind, also, that the total 
heat of the compressed steam increases 
with its pressure ; and, as this latter ap- 
proaches the boiler pressure, the tempera- 
ture of the steam in compression is also 
raised from that of about atmospheric 



148 



pressure to nearly the temperature of the 
boiler pressure. These changes of tem- 
perature which the steam undergoes will 
affect the surface of the metal with which 
the steam is in contact during the period 
of compression. It follows, of course, 
that the ends of the cylinder principally 
comprising the clearance spaces acquire a 
higher temperature than those parts where 
only expansion takes place. This is an 
important consideration, since the fresh 
steam from the boiler comes first in contact 
with these spaces ; and by touching surfaces 
which have been thus previously heated by 
the high temperature of the compressed 
steam, less heat will be abstracted from the 
live steam, and therefore a less amount of 
water be condensed in the cylinder. 

Power expended in compression lessens 
the available power of the engine, without 
necessarily lessening the efficiency of the 
steam. Under proper management, as 
stated above, the compressed steam gives 
out during its re-expansion the power di- 
rectly expended in compressing it. There 
is, no doubt, a somewhat great proportional 






149 



loss by friction ; but, to counterbalance 
this, the wasteful back-pressure is reduced 
by the earlier closing of the exhaust. 

The termination of the compression curve 
should coincide with the beginning of the 
admission line ik (see diagram Fig. 17). 

As in expansion, so in compression : the 
actual curves, as shown by the indicator dia- 
grams generally, and more especially those 
taken from locomotives, do not coincide 
with the theoretical curves. Here again the 
application of the law of Boyle and Mari- 
otte — namely, the volume of the retained 
steam being inversely as the pressure — 
comes nearest to practical results. It will 
not be difficult to account for the fact that 
the indicated compression curve should be 
below the theoretical curve. During the 
period of exhaust, the surface of the cylin- 
der-cover, piston, and cylinder have become 
materially cooled. When the exhaust-port 
closes, the pressure and temperature of the 
retained steam rapidly rise, the temperature 
of the metal in contact with it rising simul- 
taneously ; but, owing to the surfaces being 
large in proportion to the quantity of steam, 



150 



a portion of the steam will be condensed. 
This loss of compression pressure is at- 
tended by a corresponding gain of total 
useful pressure. Thus the departure of this 
curve, as well as that of the actual expan- 
sion line, below and above the theoretical 
curves respectively, shows a proportional 
increase of the power exerted by the engine, 
which is clearly demonstrated by the in- 
crease of area included in the indicator 
diagrams. 

By lead is meant the width of the open- 
ing of the steam-ports before the beginning 
of the stroke of the piston. On the steam 
side of the valve, it is called outside lead; 
on the exhaust, inside lead. 

The lead and the period of admission 
should be the same for each end of the 
cylinder, for each point of cut-off, and if 
possible, in locomotive engines, in the back 
as well as the forward gear. 

It is found necessary, especially with 
high speeds of piston, in order to insure 
good action of the steam, that the maximum 
cylinder pressure should be attained at the 
very commencement of the stroke. If the 



151 



steam-port is not opened until after the 
piston has commenced its stroke, especially 
where there is but little compression, some 
appreciable time would be consumed in 
filling the clearance space and the steam 
passages with steam. In locomotives where 
the slide-valve is worked by the ordinary 
link-motion, the steam-port will not open 
rapidly enough to enable steam of the maxi- 
mum boiler pressure to fill the space after 
the receding piston, unless the valve begins 
to open the steam-port before the piston 
begins its stroke ; that is, before the end 
of its preceding stroke. The Baldwin Loco- 
motive Works allow from -^(0.0625) to 
T 3 g- (0.1875) inch lead, according to the 
class of locomotives ; but in ordinary cases, 
from J2 (0.03125) to T V (0.0625) of an 
inch will be sufficient. 

When the maximum cylinder pressure is 
attained at the commencement of the stroke, 
the admission line of the indicator diagram 
(the piston being at the end of the stroke) 
will rise in a vertical line (see diagram Fig. 
10) ; but, if the maximum pressure is not 
so attained, the admission line will deviate 



152 



slightly from the vertical (see diagram 
Fig. 16). 

Lead and compression both regulate the 
steam admission. If the clearance space 
at the beginning of the admission is already 
filled with compressed steam, a less amount 
of lead is necessary, and vice versa. 

In locomotive engines with the shifting- 
link motion, however, not only the lead, but 
also the compression, increase rapidly as the 
link approaches mid-gear or half -stroke. 
This is not a drawback, as the increased 
compression is calculated to facilitate great- 
ly the attainment of the full pressure of 
steam in the cylinder at the commencement 
of the stroke. 

Furthermore, it should be remembered 
that a good admission of the steam depends 
not only on the amount of lead, but also on 
the commencement of it : or, in other words, 
on the period at which the valve opens the 
connection with the steam- chest preparatory 
to the next stroke of the piston. 

THE MEAN EFFECTIVE PRESSURE. 

The mean effective pressure is the differ- 



153 



ence between the mean, or average, propel- 
ling pressure, and the mean, or average, 
back-pressure. This pressure is best ob- 
tained from indicator diagrams. To arrive 
at it correctly, we divide the length of the 
card into ten or more equal spaces, so ar- 
ranged that there is a half-space at each 
end (see dotted lines, Fig. 13). Ten is a 
convenient number, but this is immaterial : 
any other number may be used. The more 
numerous the spaces, of course, the greater 
the accuracy. 

THE TERMINAL PRESSURE. 

This term is sometimes applied to the 
pressure at the exhaust-point when the 
steam is released ; but, as it is an indis- 
pensable factor in the calculations, it is 
properly defined as the pressure that would 
exist at the end of the stroke if the steam 
had not been released at that earlier point. 
A continuation of the expansion curve, as at 
g in diagram, Fig. 17 (see dotted line), will 
explain the method of finding it. Diagrams, 
Figs. 13, 15, and 16, show that the exhaust 
has taken place at the end of the stroke : 



154 



hence, in those diagrams, terminal and ex- 
haust pressure are the same. This pres- 
sure is measured from the extremity of 
the curve to the vacuum line VV: hence it 
is the absolute terminal pressure. 

THE INITIAL PRESSURE. 

The initial pressure is that pressure 
which acts upon the piston at the beginning 
of its stroke up to the point of cut-off ; and 
is always less than that of the boiler, be- 
cause as soon as the steam leaves the boiler 
it begins to condense. It can receive no 
more heat from any source ; but it must 
impart heat to every thing, and supply all 
loss resulting from radiation. A portion 
of the steam is always condensed as it 
enters the cylinder, from coming in contact 
with the surfaces which have just been 
cooled down by being exposed to the colder 
vapor of the exhaust steam. More espe- 
cially is this so in slow-running engines, 
where little or no compression takes place. 

INITIAL EXPANSION. 

Initial expansion is the expansion that 



155 



takes place during the admission of steam 
before the steam is cut off. The steam line 
&e, in diagram Fig. 16, shows considerable 
initial expansion, which is desirable in a 
" throttling " engine, — from the fact that 
saturated steam becomes superheated during 
the process of ' ' throttling, ' ' — but is not 
desirable in cut-off engines. 

WIRE-DRAWING AND THROTTLING. 

When steam is reduced in pressure by 
passing through a contracted passage, as in 
a stop- valve partly closed, or in the com- 
mon "throttle- valve," it is said to be 
"throttled," and is shown by the fall of 
the steam line Jc to e, as exhibited in dia- 
grams, Figs. 11 and 16. 

The term ' ' wire-drawing ' ' is almost 
identical in meaning with throttling, but 
refers especially to the slow cutting-off of 
steam by an ordinary slide-valve ; the result 
in the diagram being a gradual slanting 
downwards of the steam line until it passes 
imperceptibly into the expansion line. Dia- 
gram Fig. 22 is an example of this ; and 
the dotted lines show the effect of a quick 



156 



8- 



cut-off obtained by means of an expansion 
valve. 

With the ordinary valve-gearing, espe- 
cially the shifting link in common use in 
locomotive engines, or when a single eccen- 
tric connected directly to the valve-rod is 

Fig. 22. 




used, it is impossible to obtain an early 
cut-off without a certain amount of wire- 
drawing. If, under these circumstances, 
an earlier qut-off than half-stroke is at- 
tempted, wire-drawing becomes excessive. 
The above diagram, Fig. 22, taken from 



AJ 



157 



one of the most advanced types of locomo- 
tives, exhibits considerable wire-drawing. 
The clotted line shows the pressure that 
might have been obtained with the same 
amount of steam more rapidly introduced 
into the cylinder, indicating a loss from 
this cause alone of about ten per cent of the 
whole power of the engines. 

Modern automatic cut-off valve arrange- 
ments are so designed as to avoid wire- 
drawing with high rates of expansion ; the 
commonest and simplest being by means of 
double eccentrics, one of which is operated 
by the governor so as to give a sufficiently 
rapid and early cut-off. See diagrams, 
Figs. 10, 12, 13, and 15, which show a per- 
fectly steady steam line up to point of cut- 
off, with expansion through the rest of the 
stroke. 

It is an established fact, that ' c wire- 
drawing" and "throttling" are accom- 
panied by direct loss, due to the reduction 
of initial pressure which takes place during 
the process, and by indirect waste, owing 
to the increased proportion of work ex- 
pended in overcoming the back-pressure. 



158 



Aside from the economic loss, there is 
the no less serious objection to contracted 
passages, that, as the cylinder pressure is 
reduced (and therefore the power of the 
engine in the same proportion) , a large-size 
engine becomes only equal to one of less 
size, weight, and cost, with more liberal 
steam passages. 

UNDULATIONS, OR WAYINESS, OF THE EXPAN- 
SION LINE. 

The waviness sometimes seen in expan- 
sion lines is caused by the inertia of the 
indicator piston, and in some cases by 
the use of a weak indicator spring on high- 
speed engines. (See diagram Fig. 23.) 
The weaker the spring, the more rapidly the 
steam will compress it, and consequently 
the greater will be the velocity of the indi- 
cator piston in rising ; but the momentum 
(which is proportional to the square of the 
velocity) carries the piston above the point 
to which the steam pressure alone would 
have compressed the spring. When the 
momentum has been destroyed by the 
spring, the spring then forces the indicator 



159 



piston below the point where it and the 
steam would be in equilibrium ; and it is 

These alternate 



B 



again forced too high. 

Fia. 23. 




up-and-down movements produced by the 
momentum, combined with the lateral move- 
ment of the card, give the wavy line. 



~V 



160 



These lines are of great value, as they 
show precisely the degree of suddenness or 
violence of the action of the indicator. 

Fig. 24. 




^^D 



They may occur at the point of admission, 
of cut-off, and of exhaust. 

The reduced diagram, Fig. 23, taken 
from a high-speed engine running at the 
Brush Electric-Light Station, Philadelphia, 



tf 



B 



161 



Perm., in 1882, at 292 revolutions per 
minute, affords a beautiful illustration of 
this action. 

Fig. 25. 




To diminish the extent of these undula- 
tions, the spring of the indicator should be 
stiff, and its mechanism light. These un- 
dulations, when excessive, make it extreme- 
ly difficult to determine the mean effective 



162 



pressure from the diagrams when measured 
by ordinates. To determine the area, it is 
customary and more accurate to sketch a 
diagram, freed from these undulations, over 
the actual diagram taken (as represented 
by dotted lines in diagram, Fig. 24) mid- 
way between the crests and hollows of the 
waves. This is better than drawing a line 
enclosing the same area with the wavy line. 
Where the fall of the expansion line is a 
succession of steps (see diagram Fig. 25) , 
it shows slight friction in the instrument, 
and that there is no rise of the pencil, — no 
re-action. 

THE EXPANSION CURVE OF INDICATOR 
DIAGRAMS. 

A correct curve does not necessarily show 
an economical engine, since the leakage- 
out may balance the leakage-in, in rare 
cases, and not affect the diagram. But the 
opposite is indisputable : that an incorrect 
curve necessarily and infallibly shows a 
wasteful engine, to at least the amount 
calculated upon the diagram. 

As indicator diagrams represent the 



163 



measure of force, or pressure of the steam 
in the cylinder at every point of the stroke, 
the actual card from an engine, as compared 
with the theoretic diagram (other things 
being equal) , indicates the working value 
and economy of the engine. 

Therefore they should truthfully repre- 
sent the real performance of the engine. 
Diagrams vary in form, from various 
causes ; namely, quality or condition of the 
steam, leakage, condensation, adjustment, 
and construction, — their influence being 
most noticeable in the expansion curve. 
This curve will not, in practice, conform 
exactly to the true theoretical curve. The 
terminal pressure will always, under the 
most favorable conditions, be found rela- 
tively too high ; the amount being greater 
as the ratio or grade of expansion increases. 
Where this is not the case, and the expan- 
sion curve of the diagram taken coincides 
exactly with the theoretic curve, the con- 
clusion cannot be otherwise than that the 
leakage is greater than the re- evaporation ; 
but, in the present state of the arts, there 
are no practical means of working steam 



164 



expansively, and preserving the exact tem- 
perature due to the pressure while expand- 
ing. 

When the expansion curve falls through- 
out its entire length below the hyperbolic 
or theoretical curve, it is evidently due to 
leakage. The expansion curve of the in- 
dicator diagram in all ordinary cases termi- 
nates above that of the theoretical curve ; 
in fact, sometimes far above it, due to the 
re-evaporation of the moisture in the cylin- 
der. An engineer, when indicating an en- 
gine, should see to it that the piston and 
valves are tight. Unless they are so, the 
diagram will not indicate what the engine 
is really doing, and the engineer cannot 
ascertain the causes of any peculiarities in 
the form of the diagram. 



165 



CONCLUSION. 

It is hoped that enough has been said to 
present a general view of the application 
and use of the indicator, and before closing 
it may be useful to append a few general 
remarks. 

Rankin, Graham, Nystrom, and Porter, 
in their books on the steam-engine and the 
indicator, discuss a large number of causes 
which influence the form of the indicator 
diagram . 

First, The steam pressure undergoes 
some fall during the passage from the 
boiler to the cylinder. The amount of such 
fall varies greatly in different engines ; but 
the general result is that the highest aver- 
age indicated steam pressure before expan- 
sion begins is some two or three pounds 
less than the boiler pressure. 

The most important points to be noticed 
are : — 

(a) The resistance of the steam pipe 
through which the steam passes. 



166 



(b) The resistance of the throttle- valve. 

(c) The resistance clue to the ports and 
steam passages ; and here, also, the bends 
or sharp angles, as well as the imperfect 
covering, of the steam-pipe must be taken 
into account. 

All authorities agree that in the present 
state of our knowledge it is impossible to 
calculate separately the losses of pressure 
due to these causes ; and, if it were possible, 
the resulting; formulae would be too com- 
plicated to be of much use. An observation 
of this kind has a wide application. It may 
be pointed out, that steam which has been 
lowered in pressure by the resistance of 
passages (or has been ivire-draivn, as we 
have termed it) is, to some extent, super- 
heated by the friction of its molecules, the 
tendency of all friction being to produce 
heat. 

Second, There is, in practice, a rounding 
of the angle at e (see diagram Fig. 20) , at 
which the expansion curve begins. This is 
called wire-drawing at cut-off. It is always 
to be seen where the steam- valve closes 
gradually, as in diagram Fig. 22 ; but is 



167 



reduced to a minimum in the improved form 
of cut-off valves as are in general use, as 
Buckeye, Porter, Allen, and Corliss en- 
gines. Speaking generally, it may be said 
that the steam begins, as it were, to work 
expansively a little before the valve is com- 
pletely closed ; or, that the power exerted is 
nearly the same as if the valve had closed 
instantaneously at a somewhat earlier point 
of the stroke, which point may be termed 
the "effective cut-off." Such a point is 
easily obtained by carrying the expansion 
curve a little higher, and by prolonging the 
probable steam-line to meet it. 

Third, The rounding of the expansion 
curve (see diagrams, Figs. 17 and 20, at / 
to D) , when release begins before the end 
of the stroke ; and it is recommended that 
the point of exhaust release should be so 
adjusted that one-half of the fall of press- 
ure takes place at the end of the forward 
stroke, and the other half at the beginning 
of the return stroke (see Z>, d). Where 
the release is small, the expansion curve is 
continued to the end of the diagram (see 
Fig. 18). 



168 



Fourth, The general effect of water in 
the cylinder, from whatever cause pro- 
duced, but which we will suppose to be 
present in some degree throughout the 
stroke, is to lower the steam-line in the first 
portion of the stroke, and to raise it in the 
latter portion. 

Fifth, There is also the conduction of 
heat to or from the walls of the cylinder, 
the general effect of which is that in the 
last case. 

Sixth, Clearance will modify the form of 
the expansion curve of steam, by removing 
backwards through a small space the zero 
line of volumes (see diagram Fig. 17) ; 
and, as we have seen, if the steam be com- 
pletely exhausted from the cylinder during 
the return stroke, the effect of clearance is 
to waste a quantity of steam during the 
double stroke (see diagram Fig. 15). But, 
inasmuch as it is possible to compress a 
portion of the exhaust steam in the cylin- 
der during the return stroke (see diagrams, 
Figs. 18, 20, 22, and 23), the loss above re- 
ferred to may be greatly or perhaps wholly 
eliminated. 



169 



The best authorities on this subject 
recommend that the point of compression 
should be adjusted in such a manner that 
the quantity of steam confined or cushioned 
should be just sufficient to fill the clearance 
spaces with steam at the initial pressure, 
when the piston comes to rest. In such a 
case the work expended in compression 
is restored again during expansion, and 
the steam spring is continually reproduced 
without waste. 

Seventh, It will be seen by diagrams, 
Figs. 11, 16, and 22, that throttling and 
wire-drawing are accompanied by direct 
loss due to the reduction of the initial 
pressure which takes place during the pro- 
cess, and by indirect waste owing to the 
increased proportion of work expended in 
overcoming the back-pressure. 

Eighth, There is a great necessity for a 
delicate steam-engine indicator, giving con- 
tinuous diagrams on a roll of paper, similar 
to the stock-quotation indicators. 



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